Question

The linear function f(x) passes through the points (0, 3) and (2, 7) .

A few values from the exponential function g(x) are shown in the table.

x g(x)
−1 23
2 18
3 54

What is the positive difference in the y-intercept value of ​ f(x) ​and g(x) ​?

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Answer 1

1 is the positive difference in the y-intercept value of ​ f(x) ​and g(x)

Explanation:

The linear function f(x) passes through the points (0, 3) and (2, 7)

Here (0,3) is the point where f(x) crosses y axis

So y intercept = 3

Now we find g(x) from the given table

g(x) is an exponential function

General form of exponential function is g(x)= ab^x

Now we use the given values from the table

When x=2 , g(x)= 18

Plug in the values

`g(x)= ab^x` =>
`18= ab^2`(equation 1)

When x=3 , g(x)= 54

Plug in the values

`g(x)= ab^x` =>
`54= ab^3`(equation 2)

Divide second equation by first equation

`(54)/(18) = (ab^3)/(ab^2)`

so b = 3

We know 18 = ab^2

Plug in 3 for b

`18= a (3)^2`

18= 9a

Divide by 9 on both sides

So a= 2

So g(x) becomes
`g(x) = 2(3)^x`

To find y intercept we plug in 0 for x

g(x) = 2(3)^2= 2

So y intercept = 2

y intercept of f(x) is 3 and y intercept of g(x) is 2

Difference is 3-2 = 1