What statement correctly describes the key features of the graph of f(x) = −3(one third)x + 1 − 2?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 388 People

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

Answered by maham237 @ 25/12/2020

Answer: The correct option is B.

Explanation:

The given function is,

$f(x)=4(\frac{1}{2})^{(x+1)} -3$

Put x=0 to find the y-intercept.

$f(x)=4(\frac{1}{2})^{(0+1)} -3$

$f(x)=4(\frac{1}{2}) -3$

$f(x)=2-3$

$f(x)=-1$

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.

What statement correctly describes the key features of the graph of f(x) = −3(one third)x + 1 − 2?

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