Question

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Find the y-intercept of each exponential function and order the functions from least to greatest y-intercept.

Answer 1

1) g(x) ----> y-intercept -3

2) h(x) ----> y-intercept -1

3) f(x) ----> y-intercept 2

Explanation:

we know that

The y-intercept or initial value, is the value of y when the value of x is equal to zero

Calculate the y-intercept of each exponential function

case 1) A function g, has a growth factor of 2 and a value of 1, and passes through the point (1,-2)

The exponential function is equal to

`g(x)=1(2)^(x)+c`

Find the value of c

For x=1, g(x)=-2

substitute

`-2=(2)^(1)+c`

`-2=2+c`

`c=-4`

so

`g(x)=(2)^(x)-4`

Find the y-intercept

For x=0

`g(0)=(2)^(0)-4`

`g(0)=-3`

case 2) Observing the table

For x=0

f(0)=2

therefore

The y-intercept of f(x) is 2

case 3) Observing the graph

For x=0

h(0)=-1

therefore

The y-intercept of h(x) is -1

Order the functions from least to greatest y-intercept

1) g(x) ----> y-intercept -3

2) h(x) ----> y-intercept -1

3) f(x) ----> y-intercept 2