Question

1-What is the exponential function graphed in the figure?

A. ƒ(x) = 16(1⁄2)x
B. ƒ(x) = 16(2)x
C. ƒ(x) = 16(2)x
D. ƒ(x) = 16(1⁄2)x


2-
Write the equation of the graphed function.



A. y = 5⁄4x – 3
B. y = 4⁄5x + 3
C. y = 5⁄4x + 3
D. y = 4⁄5x – 3

3-
What is the exponential function graphed in the figure?



A. h(x) = 3(1⁄2)x
B. h(x) = 3(2)x
C. h(x) = 3(2)x
D. h(x) = 2(3)x

Answer 1

1. The required function is
`f(x)=16((1)/(2))^x`.

2. The required function is
`y=(5)/(4)x-3`.

3. The required function is
`h(x)=3(2)^x`.

Explanation:

1.

The exponential function is defined as

`f(x)=ab^x`

Where, a is initial value and b is growth rate.

The y-intercept of the given graph is (0,16) and the graph shows a decreasing function. So, the initial value is 16 and growth rate is less than 1.

The required function is

`16((1)/(2))^x`

2.

The y-intercept of the function is (0,-3).

The line is passing through (0,-3) and (4,2). The slope of the line is

`m=(y_2-y_1)/(x_2-x_1)=(2-(-3))/(4-0)=(5)/(4)`

The slope intercept form of a line is

`y=mx+b`

Where, m is slope and b is y-intercept.

The required function is

`y=(5)/(4)x-3`

3.

The exponential function is defined as

`f(x)=ab^x`

Where, a is initial value and b is growth rate.

The y-intercept of the given graph is (0,3) and the graph shows a increasing function. So, the initial value is 3 and growth rate is greater than 1.

The required function is

`h(x)=3(2)^x`