Question

Given that g(x) is a transformation of f(x)=x, use the table to write the equation of g(x).

Answer 1

Answer: g(x) = f(x) - 3

Explanation:

We know f(x) = x

Subtracting 3 from the x value/f(x) equals g(x) column

-8 - 3 = -11

-4 - 3 = -7

0 - 3 = -3

4 - 3 = 1

8 - 3 = 5

Answer 2

The equation for g(x) based on the transformation of f(x)=x is:

g(x)=f(x)−3

g(x)=x−3

The transformation from f(x)=x to g(x) appears to be a shift downward by 3 units. Let's examine how the values change.

f(x)=x

g(x)=f(x)−3

Using the given values for x and g(x):

For x=−8, f(−8)=−8 and g(−8)=−11

−8−3=−11 - This fits the transformation.

For x=−4, f(−4)=−4 and g(−4)=−7

−4−3=−7 - This fits the transformation.

For x=0, f(0)=0 and g(0)=−3

0−3=−3 - This fits the transformation.

For x=4, f(4)=4 and g(4)=1

4−3=1 - This fits the transformation.

For x=8, f(8)=8 and g(8)=5

8−3=5 - This fits the transformation.

Therefore, the equation for g(x) based on the transformation of f(x)=x is:

g(x)=f(x)−3

g(x)=x−3