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3 years ago

What is the range of f(x) = 4^x?

Mathematics

1 answer:

Oxana [17]3 years ago

5 0

Answer: A because it goes from (0,infinity) so all positive real numbers

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HELP with these questions

zlopas [31]

Step-by-step explanation:

transform the parent graph of f(x) = ln x into f(x) = - ln (x - 4) by shifting the parent graph 4 units to the right and reflecting over the x-axis

(???, 0): 0 = - ln (x - 4)

$\frac{0}{-1} = \frac{-ln (x - 4)}{-1}$

0 = ln (x - 4)

$e^{0} = e^{ln (x - 4)}$

1 = x - 4

+4 +4

5 = x

(5, 0)

(???, 1): 1 = - ln (x - 4)

$\frac{0}{-1} = \frac{-ln (x - 4)}{-1}$

1 = ln (x - 4)

$e^{1} = e^{ln (x - 4)}$

e = x - 4

+4 +4

e + 4 = x

6.72 = x

(6.72, 1)

Domain: x - 4 > 0

+4 +4

x > 4

(4, ∞)

Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that

No vertical asymptotes

*************************************************************************

transform the parent graph of f(x) = 3ˣ into f(x) = - 3ˣ⁺⁵ by shifting the parent graph 5 units to the left and reflecting over the x-axis

Domain: there is no restriction on x so domain is all real number

(-∞, ∞)

Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0. the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.

(-∞, 0)

Y-intercept is when x = 0:

f(x) = - 3ˣ⁺⁵

= - 3⁰⁺⁵

= - 3⁵

= -243

Horizontal Asymptote: y = 0 (explanation above)

5 0

3 years ago

Danni is training for a marathon. Her target speed is 25 miles per hour. She currently runs 15 miles in 1/2 and hour. Does she a

Andrews [41]

Yes because if it’s fifteen in 1/2 an hour you multiply by two she is at 30 miles an hour which surpasses her goal by five

6 0

2 years ago

A farmer wants to use 200 feet of fencing for a chicken pen. He wants the width of the pen to be 20 feet. What is the length of

Aneli [31]

The length should be 80 feet.

This is because the width is 20, since there are two sides for the width in a pen, we have to add 20+20. This would equal 40. Then we need to subtract 40 from 200. 200-40 would be 160. Then since there are two sides for the length, we need to split that in half. 160÷2 would be 80. To double check, you can do 80+80 and that would still be 160. So the length of one side would be 80. But of course, this whole thing would only be right if the pen has four sides(but since i have seen many chicken pens, there were all rectangular). I hope this helped! :)

7 0

2 years ago

Please help! thanks :)

Evgen [1.6K]

If you times 39.99 by 0.20 (20%) then you get your answer of $7.99

4 0

2 years ago

Line r has a slope of -5/2 line s has a slope of 2/5 are line r and line parallel or perpendicular

Elis [28]

Vocab:
Parallel = same slope
Perpendicular = opposite sign and reciprocal slope

-5/2 opposite and reciprocal = 2/5

Solution: they are perpendicular

4 0

3 years ago