Question

What are the asymptote and the y-intercept of the function shown below? F(x) = 6(0.5)x + 2 A. Asymptote: y = 1 y-intercept: (0,5) B. Asymptote: y = -2 y-intercept: (0,8) C. Asymptote: y = 2 y-intercept: (0,8) D. Asymptote: y = 2 y-intercept: (0,5)

Answer 1

Answer:

Asymptote: y = 2 y-intercept: (0,8)

Step-by-step explanation:

The given function is

$f(x) = 6(0.5)^{x} + 2$

This function is of the form:

$f(x) = a {b}^{x} + c$

where y=c is the horizontal asymptote.

By comparing , we have c=2 hence the horizontal asymptote is

$y = 2$

To find the y-intercept, we put x=0 into the function to get:

$f(0) = 6(0.5)^{0} + 2 = 6 + 2 = 8$

Therefore the y-intercept is (0,8).

Answer 2

The asymptote of the function is y = 2 and the y-intercept of the function is (0,8)

How to determine the asymptote?

The equation of the function is given as:

f(x) = 6(0.5)^x + 2

Set the exponential part to 0

f(x) = 0 + 2

This gives

f(x) = 2

Hence, the asymptote of the function is y = 2

How to determine the y-intercept?

The equation of the function is given as:

f(x) = 6(0.5)^x + 2

Set x to 0

f(0) = 6(0.5)^0 + 2

This gives

f(0) = 8

Hence, the y-intercept of the function is (0,8)

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