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aliya0001 [1]
3 years ago
13

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

Mathematics
1 answer:
earnstyle [38]3 years ago
6 0

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



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