Question

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

Answer 1

Answer:

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

Step-by-step 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

$\frac{54}{18} = \frac{ab^3}{ab^2}$

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