(Select all that are correct) which statements describe key features of function g if g(x) = f(x + 2)
a. y-intercept at (0,4)
b. domain of {x|-♾️< x <♾️}
c. horizontal asymptote of y = 0
d. horizontal asymptote of y=2
e. y-intercept at (0,1)
Answers
Answer:
Y-intercept (0,1) / Domain (-infinite,infinite) / horizontal asymptote y=0
The y-intercept is: (0,1)
The domain is [tex]\{x|-\infty < x < \infty\}[/tex]
The horizontal asymptote is [tex]y = 0[/tex]
The given parameters from the complete question are:
[tex]f(x) = 2^{x-2}[/tex]
[tex]g(x) = f(x + 2)[/tex]
First, we calculate the function of g(x)
[tex]g(x) = f(x + 2)[/tex]
Calculate f(x + 2)
[tex]f(x) = 2^{x-2}[/tex]
[tex]f(x + 2) = 2^{x+2-2}[/tex]
[tex]f(x + 2) = 2^x[/tex]
So:
[tex]g(x) = 2^x[/tex]
Start by calculating the y intercept:
This means, we calculate the g(x) when [tex]x=0[/tex]
[tex]g(x) = 2^x[/tex]
[tex]g(0) = 2^0[/tex]
[tex]g(0) =1[/tex]
The above computation means (a) is incorrect; but (e) is correct.
Next, calculate the domain of g(x)
[tex]g(x) = 2^x[/tex]
Some features in a function that limit the x values are: roots, fractions, etc.
[tex]g(x) = 2^x[/tex] does not have any restricting value of x.
This means the value of x ranges from negative infinity to positive infinity.
Hence, the domain is: [tex](-\infty,\infty)[/tex]
The above computation means (b) is correct
Next, calculate the horizontal asymptote.
To do this, we plot the graph of g(x) --> see attachment
Then we trace a horizontal line from the horizontal part of the curve of g(x) till it gets to the y-axis.
From the attached graph of g(x), the line touches the y-axis at [tex]y = 0[/tex]
So, the horizontal asymptote is: [tex]y = 0[/tex]
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Related Questions
Mole Conversion:
What is the mass of 3.13 x 1023 molecules of carbon dioxide?
Answers
Answer:
The mass of 3.13*10²³ molecules of carbon dioxide is 22.88 g.
Step-by-step explanation:
Avogadro's Number or Avogadro's Constant is the number of particles that make up a substance (usually atoms or molecules) and that can be found in the amount of one mole of said substance. Its value is 6.023*10²³ particles per mole and it applies to any substance.
Then you can apply the following rule of three: if 6.023*10²³ molecules are present in 1 mole, 3.13*10²³ molecules are present in how many moles?
[tex]moles=\frac{3.13*10^{23}molecules*1 mole }{6.023*10^{23}molecules}[/tex]
moles= 0.52
Since the molar mass of carbon dioxide is 44 g / mole, then the following rule of three can be applied: if there are 44 g in 1 mole, how much mass is there in 0.52 moles?
[tex]mass=\frac{0.52 moles*44 g}{1 mole}[/tex]
mass= 22.88 g
The mass of 3.13*10²³ molecules of carbon dioxide is 22.88 g.
PLEASE HELP MEEEEE!!! IT's TIMED
Answers
Answer:
x is less than oe equal to 12
Answer:
x ≤ 15
Step-by-step explanation:
7x - 6 ≤ 3x + 54
Subtract 3x from both sides;
4x - 6 ≤ 54
Add 6 to both sides;
4x ≤ 60
Divide both sides by 4;
x ≤ 15
7
Which two whole numbers is 20 between?
Answers
Answer:
19 and 21
Step-by-step explanation:
... 17, 18, 19 , 20, 21, 22, 23 ,24, 25
Given that [tex](ax+4)(2x+b)=2x^2+5x-12[/tex], what are the values of a and b?
Answers
Answer:
a = 1, b = - 3
Step-by-step explanation:
Expand the factors on the left side, then compare the coefficients of like terms on both sides.
left side
(ax + 4)(2x + b) ← expand using FOIL
= 2ax² + abx +8x + 4b
= 2ax² + x(ab + 8) + 4b
Compare coefficients of like terms with those on right side.
coefficients of x² terms
2a = 2 ( divide both sides by 2 )
a = 1
comparing constant terms
4b = - 12 ( divide both sides by 4 )
b = - 3
Please help is this a solution or inequality 5-x<8;x=-3
Answers
Answer:
Its a inequality
Step-by-step explanation:
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The two expressions we have is ‘5 - x’ and ‘8’. If X is equal to three, then we get ‘5 - 3’ and ‘8’. This comes out to 2 > 8.
Hope this helps :)
A pre-image arrow pointing east is rotated 135° clockwise. In which direction is the image arrow pointin
Answers
Given :
A pre-image arrow pointing east is rotated 135° clockwise.
To Find :
In which direction is the image arrow point.
Solution :
90° clockwise shift make it south.
Now, remaining angle for rotation ( 135 - 90 )° = 45°.
So, direction of moving 45° more clockwise makes it 45° west of south or 45° south of west.
Hence, this is the required solution.
Suppose IQ scores were obtained from randomly selected couples. For 20 such pairs of people, the linear correlation coefficient is 0.907 and the equation of the regression line is y=9.88+0.9x, where x represents the IQ score of the husband. What is the best predicted IQ of the wife, given that the husband has an IQ of 101?
Answers
Answer:
108.88
Step-by-step explanation:
Given that:
Equation of Regression line obtained for couple's IQ:
y=9.88+0.9x
x represents the IQ score of the husband
The best predicted IQ of wife Given that husband's IQ is 110
y = 9.88 + 0.9(110)
y = 9.88 + 99
y = 108.88
please yall im crying this is hard
Answers
Answer:
I think ur and is 4140. but I'm not sure, sorry if its incorrect.
what is the common fraction of the decimal 0,76
Answers
Answer:
76/100
Step-by-step explanation: 76 is in the hundreds place
y=-4/7x+2 is it Proportional
Constant of proportionality: k=
Not proportional
URGENT
Answers
Answer:
It is
5/7
Explanation:
The number
5/7
tells you that when
x
increases of
1
then
y
always increases of
5/7
.
Graphically:
graph{7/7*x [-10, 10, -5, 5]}
Step-by-step explanation:
LaShea would like to invest her $100 in birthday money. Which option will give her the most money at the end of the investment period?
1 year at 8 percent
1.5 years at 7 percent
2 years at 6.5 percent
3 years at 4 percent
Answers
Answer:
1 year at 8 percent
Step-by-step explanation:
i took the test
Factor 14x−24 using the GCF
Please help me! Hurry! Please show your work.
Answers
Answer:
2(7x - 12)
Step-by-step explanation:
Find the GCF of 14 and 24: 2Divide each number by 2 shown in steps 3 and 414x ÷ 2 = 7x24 ÷ 2 = 12Re-write the expression: 2(7x - 12)I hope this helps!
A parking lot that has 520 spaces
was filled with 390 cars. What
percent of the parking lot was full?
Answers
Answer:
75%
Step-by-step explanation:
390/520 = 0.75 =75
hope that helps ;)
Answer:
75%
Step-by-step explanation:
390/520×100%
0.75×100%
75%
Will give brainlyest Will give brainlyest Will give brainlyest Will give brainlyest Will give brainlyest.idk and if you give me the answer can you tell me if I put it on the far right or left
Answers
Answer:
so i tried to draw it.
Step-by-step explanation:
Answer:
left
Step-by-step explanation:
plz i need 4 more brainlyests to pass
What is the range of the relation below?
Answers
Answer:
D.
Step-by-step explanation:
because the lowest y is -3 and the highest is 2
Ella is putting her savings into a retirement fund that will compound her $7000 semiannually at 7% interest. How much will her retirement fund be worth after 10 years? *
Answers
Answer:
8099
Step-by-step explanation:
PLEASE I NEED IMMEDIATE HELP I will give brainliest
BD=16 and ÁT is the
perpendicular bisector of BD
BC=
Answers
Answer:
8
Step-by-step explanation:
16/2=8
Answer:
8
Step-by-step explanation:
A bisector bisects a line in HALF. Thus, by dividing 16 in half you will get BC=8.
solve for x 5(4x-5)+3x-1=20
Answers
Step-by-step explanation:
20x-25+3x-1=20
20x+3x=20+25+1
23x=46
X=2
Answer:
x=2
Step-by-step explanation:
5(4x-5)+3x-1=20 (given)
20x - 25 + 3x -1 = 20 (distribute)
23x -26 = 20 (combine like terms)
23x = 46 (add)
x=2 (division)
What is x-2+5x
What is -4x-10+6x
What is 7+10x+4x-8
Answers
Answer:
What is x-2+5x = 6x-2
What is -4x-10+6x = 2x-10
What is 7+10x+4x-8 = -4x+9
Step-by-step explanation:
Quickly XD!
3 friends share 2 pizzas evenly.
About how much pizza will each friend get?
Sorry if you tryna enjoy your weekend I Needa get this done.
Answers
y=2/3 orange for each friend (decimal: 0.6667 rounded to 4d. p)
PREMISES
y=the fraction of 2 oranges that each of 3 friends shares equally
CALCULATIONS
To distribute 2 oranges equally between 3 friends requires that the oranges be sliced proportionately equal to the number of friends which is 3
So, then,
y=
Each friend receives 1/3 of each of 2 oranges making 2/3 orange for each friend.
If y=2/3 orange, then the equations
3*2/3 orange=2 oranges
6/3 oranges=2 oranges and
2 oranges=2 oranges prove the solution y=2/3 orange to the fraction of 2 oranges shared by each of 3 friends
factor completely, 0.2x + 0.8 a. x b. 0.8(x + 1) c. 0.2(x + 1) d. 0.2(x + 4)
Answers
Answer:
d. 0.2 ( x + 4 )
Step-by-step explanation:
0.2x + 0.8
Both 0.2x and 0.8 have a common factor of 0.2, hence pull 0.2 out.
0.2x + 0.8
0.2 ( x + 4 )
) Solve this equation: − 10 + = 8 + 2 − 18
Answers
Answer:
I think the question is wrong check ur question and I will answer
By the square property, if b is a real number , and a2=b, then a=
Answers
Answer:
[tex]a=\sqrt{6},\:a=-\sqrt{6}[/tex]
Step-by-step explanation:
Given
b is a real number[tex]a^2=b[/tex]as
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
so
[tex]a^2=6[/tex]
[tex]a=\sqrt{b},\:a=-\sqrt{b}[/tex]
Therefore,
[tex]a=\sqrt{6},\:a=-\sqrt{6}[/tex]
Answer:
lal
Step-by-step explanation:
ap3x
HELP PLS this is my last question
Answers
Answer:
The solutions to the system of the equations are:
[tex]y=1,\:x=3[/tex]
Step-by-step explanation:
Given the equations
[tex]y=\frac{2}{3}x-1;\:y=-x+4[/tex]
solving the system of equation
[tex]\begin{bmatrix}y=\frac{2}{3}x-1\\ y=-x+4\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y-\frac{2}{3}x=-1\\ y+x=4\end{bmatrix}[/tex]
[tex]y+x=4[/tex]
[tex]-[/tex]
[tex]\underline{y-\frac{2}{3}x=-1}[/tex]
[tex]\frac{5}{3}x=5[/tex]
[tex]\begin{bmatrix}y-\frac{2}{3}x=-1\\ \frac{5}{3}x=5\end{bmatrix}[/tex]
solving for x
[tex]\frac{5}{3}x=5[/tex]
[tex]5x=15[/tex]
Divide both sides by 15
[tex]\frac{5x}{5}=\frac{15}{5}[/tex]
[tex]x=3[/tex]
[tex]\mathrm{For\:}y-\frac{2}{3}x=-1\mathrm{\:plug\:in\:}x=3[/tex]
[tex]y-\frac{2}{3}\cdot \:3=-1[/tex]
[tex]y-2=-1[/tex]
Add 2 to both sides
[tex]y-2+2=-1+2[/tex]
[tex]y=1[/tex]
Therefore, the solutions to the system of the equations are:
[tex]y=1,\:x=3[/tex]
PLS HELP! DUE TODAY! I WILL GIVE BRAINLIEST!
In the following activity, match each pair of equivalent expressions.
3(x + 5)
9x - 2(3x - 3)
(x + 14) - (8 - 2x)
(7 - 2x) + (3x - 11)
(7 + 5x) + (-4x - 1)
-2x + 9 + 5x + 6
-4(x + 1) + 5x
-7 + 6x - 4x + 3
2(x - 2)
-3x + 6 + 4x
Answers
Answer:
Matches are:
1 and 6
2 and 3
4 and 7
5 and 10
8 and 9
Step-by-step explanation:
First just expand all:
1. 3x + 15
2. 3x + 6
3. 3x +6
4. x - 4
5. x + 6
6. 3x +15
7. x - 4
8. 2x - 4
9. 2x - 4
10. x + 6
Please give brainliest! Thanks, hope this helps!
Morag typed 60 words in one minute. Express as a unit rate.
Answers
Answer:
60 words per minute...60/1...this is already in unit rate form
6p = 3p + 2p + p is true for
Answers
Answer:
For any value
Step-by-step explanation:
Answer:
Anything substituted for p should be correct
Step-by-step explanation:
Find the square of each imaginary number.
(Get rid of the i)
Answers
Answer:
- 32/21 over 5 is
Step-by-step explanation:
*gets coins and runs to the store to get "milk"
Answer:
-765/25
Step-by-step explanation:
please help
answer choices are:
a (-2,-8)
b (2,-8)
c (2,-4)
d. (-2,4)
Answers
What is a common tip percentage amount that people receive?
Answers
Answer:
15-20%
Step-by-step explanation:
can u make me brainiest thanks