let f(x)=4^x. The new function g(x)=f(x-1)+3 represents transformations that were made to function f. Type the new equation for g. g(x)=___
Describe the two types of transformations that occur between function f and function g. (use words like up, down, left, right, compression or stretch in your answer.)
Answers
Answer:
g(x) = [tex]4^{(x-1)}+3[/tex]
Step-by-step explanation:
Given exponential function is,
f(x) = [tex]4^{x}[/tex]
If the given function is shifted 1 unit to the right,
h(x) = f(x - 1)
= [tex]4^{(x-1)}[/tex]
If the function 'h' is shifted 3 units up,
g(x) = h(x) + 3
= [tex]4^{(x-1)}+3[/tex]
Therefore, transformed function will be,
g(x) = [tex]4^{(x-1)}+3[/tex]
Related Questions
Consider the line y = 3x - 1.
Find the equation of the line that is perpendicular to this line and passes through the point (-8, 3)
Find the equation of the line that is parallel to this line and passes through the point (-8, 3).
Answers
Answer:
y = -1/3x + 1/3
Step-by-step explanation:
The slopes of perpendicular lines are negative reciprocals.
The given line is
y = 3x - 1
This equation is written in the slope-intercept form, y = mx + b, where m is the slope.
slope of given line = m = 3
slope of perpendicular line = -1/3
Now we need the equation of the line with slope -1/3 that passes through the point (-8, 3)
y = mx + b
y = -1/3x + b
3 = (-1/3)(-8) + b
3 = 8/3 + b
9/3 = 8/3 + b
b = 1/3
y = -1/3x + b
y = -1/3x + 1/3
A construction company uses the function f(x), where x is the number of people working on a project, to model the amount of money it spends to complete a project. What would a reasonable domain be?
All integers
Real numbers
Positive real integers
Positive integers
Answers
Answer:
Please use "^" to denote exponentiation: f(x) = x^2 + 3x + 5.
Because this is a polynomial, the domain consists of the set of all real numbers.
Step-by-step explanation:
Answer:
Positive integersStep-by-step explanation:
The domain is the people and the range is the money spent
People would be counted as positive integers, only the last answer choice considers this.
So the answer is:
Positive integersSolve the equation 3(x-6)+8=5x-6
Answers
Answer:
x=-10
Step-by-step explanation:
3(x-6) +8=5x-6=
3x-18+8=5x-6=
3x-10=5x-6=
3x-5x=10-6=
-2x=4
x=-2
Answer:
x = -2
Step-by-step explanation:
3(x - 6) + 8 = 5x - 6
Distribute;
3x - 18 + 8 = 5x - 6
Collect like terms;
3x - 10 = 5x - 6
Subtract 5x from both sides;
-2x - 10 = -6
Add 10 to both sides;
-2x = 4
Divide both sides by -2
x = -2
Solve 4x + 1 = 3 – 2x
Answers
Answer:
x = 1/3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
4x + 1 = 3 - 2x
Step 2: Solve for x
Add 2x on both sides: 6x + 1 = 3Subtract 1 on both sides: 6x = 2Divide 6 on both sides: x = 1/3Step 3: Check
Plug in x to verify it's a solution.
Substitute: 4(1/3) + 1 = 3 - 2(1/3)Multiply: 4/3 + 1 = 3 - 2/3Add/Subtract: 7/3 = 7/3Here we see that 7/3 does indeed equal 7/3.
∴ x = 1/3 is a solution of the equation.
Answer:
x=1/3
Step-by-step explanation:
4x+1=3-2x
Add 2x to both sides
6x+1=3
Subtract 1 on both sides
6x=2
x=2/6
PLEASE HELPP!!!
5, 18, 6, 18, 13 find the interquartile range (SHOW WORK)
Answers
Answer:
12
Step-by-step explanation:
The interquartile range is the difference between the upper quartile and the lower quartile.
Firstly find the median of the data.
The median is the middle value of the data arranged in ascending order. If there is no exact middle value then it is the average of the values either side of the middle.
5, 6, 13, 18, 18 ← data in ascending order
↑ middle value
median = 13
The upper quartile Q₃ is the middle of the data to the right of the median
13, 18, 18
↑ middle value
Q₃ = 18
The lower quartile Q₁ is the middle value of the data to the left of the median
5, 6, 13
↑ middle value
Q₁ = 6
Interquartile range = Q₃ = Q₁ = 18 - 6 = 12
It is recommended that a certain medicine be stored in temperatures above 34°F and below 71°F. Enter a
compound inequality to show the acceptable storage temperatures for this medicine. Use t as your
variable.
Answers
Answer:
The inequality is;
34°F < t < 71°F
Step-by-step explanation:
Here, using t as the variable, we want to write an inequality
We want to write an inequality above 34 but below 71
The inequality will be;
34°F < t < 71°F
Mr.Johnson is building a dollhouse for his daughter that is a replica of his own house. His house is 48 feet long and 36 feet wide. If he makes the dollhouse 4 feet long, how wide will it be
Answers
Answer:
x=3
Step-by-step explanation:
Proportion: 48/36=4/x. (4*36)/48=x x=3.
Hope this helps plz hit the crown :D
10x+8(1/3 x + 2/3) =-20
Answers
Answer:
hiii
Step-by-step explanation:
1. Multiply both sides by 3
38/3x x 3 +16/3. x =-20x3
2. Simplfy
38x+16=-60
3. Subtract 16 from both sides
38x+16-16=-60-16
4. Simplfy
38x=-76
5. Divide both sides by 38
38x/38=-76/38
6. Simplfy
x=-2
Brainliest 5 stars thanks!
Answers
Answer:
B
Step-by-step explanation:got 100%
Answer:
B
Step-by-step explanation:
Sam’s parents agreed to pay 25 percent of the cost of a new bike if Sam paid the rest.
Percents
Total
25%
25%
25%
25%
100%
$65
$65
$65
$65
If Sam’s parents paid $65, what was the price of Sam’s new bike?
$130
$195
$260
$325
Answers
Answer:
$260
Step-by-step explanation:
From Brainly
Can I have brainliest
Answer:
The answer is 260
Step-by-step explanation:
The people paid 25% that should be 1/4 so add 65 three more times.
Pls help this is a test and I can’t go back
Answers
Answer:
Its = -5
Step-by-step explanation:
WILL GIVE BRAINLEST!!!!!!!!!!!!!!! The three graphs represent the types of solutions that are possible for a system of equations. Which graph represents a system of equations with no solution?
Answers
Answer:
its the 2nd one
Step-by-step explanation:
just did it on edge
Raven needs new winter boots. Both ShoeTown and LaceUp shoe stores carry the boots she wants to buy. The boots are regularly priced $85.95, but both stores are running sales. ShoeTown has the boots marked down 15%. LaceUp has the boots marked down 10%, plus Raven has a $5 coupon she can use on the boots after the mark down is applied.Raven’s friend, Becca, tells Raven there is an online shoe store called Run, Don’t Walk that has the boots she wants for only $71.99. If Raven buys the boots in a local store, she will have to pay 7.16% sales tax on her purchase. If Raven buys the boots online, she won’t have to pay sales tax, but she will have to pay $6.50 for shipping.
Answers
Raven should buy the boots at Shoe Town because this offers the best final price.
To determine which one is the best store for Raven let's calculate the price in each case.Shoe TownTotal price:
Initial price - Mark down + Sales tax
85.95 - 15% + 7.16 %85.95 - 12.89 + 7.16 %73.06 + 7. 16%73.06 + 5.23 = 78.29Lace UpTotal price:
Initial price - Mark down - Coupon + Sales tax
85.95 - 10% - 5 + 7.15%89.95 - 8.99 - 5 + 7.15%80.96 - 5 + 7.15%75.96 + 7.15%75.96 + 5.43 = 81.39Run, Don't WalkTotal price:
Initial price + shipping
71.99 + 6.50 = 78.45
Learn more about price in: https://brainly.com/question/2289757
what is 5 times x simplifed
Answers
Answer:5x
Step-by-step explanation:
Answer: 5x
Step-by-step explanation:
We would need to know what X is first. For example, is X is 7; 5 times x (7)
Would equal 35
5x7=35
but we don't know what X is so we leave it as 5x
According to the synthetic division below, which of the following statements
are true?
Check all that apply.
Answers
The question is not complete, so i have attached it.
Answer:
Options A, B & E are correct
Step-by-step explanation:
In the synthetic division attached, we see that:
: 2 , -2 & -12 are the coefficient of the dividend of the function 2x² - 2x - 12
: The divisor is 3
Thus;
x = 3 is a root of f(x) = 2x² - 2x - 12
Thus, (x - 3) is a factor of the dividend which is the function f(x) = 2x² - 2x - 12
- Now, from the attached image, the coefficients of the quotient are 2 , 4
- The quotient will be 1 degree less than the dividend since it was divided by the factor (x - 3)
The degree of the dividend will be 2 since it contains x²
Thus, the degree of the quotient will be 1
Therefore, the quotient in factor form is (2x + 4)
Looking at the given statements in the options;
- Option A is true, because we have established earlier that 3 is a root of f(x) = 2x² - 2x - 12
- Option B is true because we have established that (x - 3) is a factor of 2x² - 2x - 12
- Option C is not true because the factor is (x + 3) and not (x - 3)
-Option D is not true because the root is 3 and not -3
- Option E is true because we have established that quotient as a factor is: (2x + 4)
Thus, the correct options are A , B , E
9. Marika Perez's gross biweekly pay is $2,768.00 How much does she earn annually.
$66,432.00
$71,968.00
O $33,216.00
$143,936.00
Answers
Answer:
$66,432.00
Step-by-step explanation:
I believe its this sorry if I'm wrong
A local Little league has a total of 60 players, 80% of who are right-handed. Write and solve a proportion that could be used to determine how many of the players are right-handed.
Answers
Answer:
48 people are right handed. 12 are left handed
Step-by-step explanation:
80% of 60 is 48.
Find the value of x?
Answers
Answer:
C
Step-by-step explanation:
The 2 base angles in the triangle are congruent thus the triangle is isosceles.
Then the 2 sides are congruent in an isosceles triangle, thus
x = 12 → C
What measurement is the quantity of mass per unit volume?
Volume
Temperature
Mass
Density
Answers
Answer:
i thank this will help sorry if this is not right it is density.Step-by-step explanation:
please help me find what to plot for this (no decimals )
Answers
Answer:
(0, 6), (4, 5)
Step-by-step explanation:
graph (0, 6) first, then from those points go down -1 and over 4 to get (4, 5)
Which of the following is the value of e^2 correct to 3 decimal places
A:73.890
B:7.3893
C:7.389
D:738.9
Answers
Answer:
C
Step-by-step explanation:
6th grade math! Emily made 8 field goals in 25 attempts. What decimal represents the number of field goals she made?
Answers
Answer:
3.125
Step-by-step explanation:
I had use a calulator I'm sorry if I'm
Answer:
0.32
PLEASE MARK BRAINLIEST
do you play fornite
9if yes then add me
r5qtrr
Answers
Answer:
i do but cant now
Step-by-step explanation:
When a baby was born, he weighed 5.2 pounds, After two weeks, he
weighs 7.8 pounds. What is the percent of increase in the baby's weight
from the time he was born to two weeks later? *
Answers
Answer:How much weight should newborns gain?
A healthy newborn is expected to lose 7% to 10% of the birth weight, but should regain that weight within the first 2 weeks or so after birth. During their first month, most newborns gain weight at a rate of about 1 ounce (30 grams) per day.
Step-by-step explanation:
PLEASE I NEED HELP PLEASE 1. The table below shows 3 recipes for a fruit punch
flavored drink. Will all 3 recipes taste the same? (hint:
Write each ratio as a fraction then simplify to see which
are equivalent ratios)
2. Will any of them taste different?
✓
Be sure to use the vocabulary word: EQUIVALENT
RATIOS in your answer.
water
cups
1
3
4
12
1
6
18
OR
Answers
Answer:
1. It can clearly observed that all the ratios that are written in fractional form simplify to same fraction which means that all the ratios are equivalent.
2. None of them will taste different as the ratios are same.
Step-by-step explanation:
First of all we have to write the three ratios as fractions to see if the ratios are equivalent ratios or not.
We will see the water to cups ratio
The ratios in fractional form are:
[tex]=\frac{1}{3}\\=\frac{4}{12}\\=\frac{6}{18}[/tex]
Putting all the ratios together
[tex]\frac{1}{3} = \frac{4}{12} = \frac{6}{18}\\\frac{1}{3} = \frac{1}{3} = \frac{1}{3}[/tex]
1. It can clearly observed that all the ratios that are written in fractional form simplify to same fraction which means that all the ratios are equivalent. All the recipes will taste same.
2. None of them will taste different as the ratios are same.
-12+8yi=3x-i solve for x and y
Answers
Answer:
x = -4 + 8yi/3 + i/3, y = -3xi/8 - 1/8 - 3i/2
please help me solve this
Answers
x<3
semoga membantu
dan maaf kalo salah
Answer:
X>_3 the first one
Step-by-step explanation:
It is rather equal to 3 or less
12 less than the square of a number
Answers
Answer:
uh what?
Step-by-step explanation:
Given the table. Answer the following questions given the original function f(x).
2.
3
5
6
X
-3
-2.
-
0
1
2.
3
4
5
f(x)
8
7
6
5
4
3
2
1
0
8
What is the value of f1(7)?
Answers
Answer:
f(x)
Step-by-step explanation:
(I’ll give brainliest) plz ASAP
Answers
Answer:
i can't read it, plz zoom in next time