Question

What statement correctly describes the key features of the graph of f(x) = 4(one half)x + 1 − 3?

A. Y-intercept of (0, −1), starts up on the left, gets closer to y = −3 on the right
B. Y-intercept of (0, −1), starts down on the left, gets closer to y = −3 on the right
C. Y-intercept of (0, 1), starts up on the left, gets closer to y = −3 on the right
D. Y-intercept of (0, 1), starts down on the left, gets closer to y = −3 on the right

Answer 1

Answer: the correct answer is B

Step-by-step explanation:

Answer 2

Answer: The correct option is B.

Step-by-step explanation:

The given function is,

`f(x)=4((1)/(2))^((x+1)) -3`

Put x=0 to find the y-intercept.

`f(x)=4((1)/(2))^((0+1)) -3`

`f(x)=4((1)/(2)) -3`

`f(x)=2-3`

`f(x)=-1`

At x=0 the value of f(x) is -1, therefore the y- intercept is (0,-1).

Since it is an exponential function in the form of,

`g(x)=ma^x+n`

Where, 0<a<1, so,

`f(x)\rightarrow \infty\text{ as }x\rightarrow -\infty`

`f(x)\rightarrow -3\text{ as }x\rightarrow \infty`

Therefore the starts up on the left, gets closer to y = −3 on the right. So the option B is correct.