Transforming Linear Functions

Question

Given f(x)=6x+5​, describe how the graph of g compares with the graph of f.

g(x)=6(0.2x)+5

Select the correct choice below, and fill in the answer box to complete your choice.

A. The graph of​ g(x) is translated _ ​unit(s) to the left compared to the graph of​ f(x).

B. The graph of​ g(x) is translated _ ​unit(s) down compared to graph of​ f(x).

C. g(x) has a scale factor of _ compared to​ f(x). Because it scales the vertical​ direction, the graph is stretched vertically.

D. g(x) has a scale factor of _ compared to​ f(x). Because it scales the vertical​ direction, the graph is compressed vertically.

E. g(x) has a scale factor of _ compared to​ f(x). Because it scales the horizontal​ direction, the graph is stretched horizontally.

F. g(x) has a scale factor of _ compared to​ f(x). Because it scales the horizontal​ direction, the graph is compressed horizontally.

G. The graph of​ g(x) is translated _ ​unit(s) to the right compared to the graph of​ f(x).



H. The graph of​ g(x) is translated _ ​unit(s) up compared to graph of​ f(x).

Answer 1

We write y = A(x+B) + C to define the transformation of the linear equation.

In this case, B=0, so no shift left or right on the x-axis.

C=5 in both equations, so no shift up or down on the y-axis.

The only change is A, from 6 to 6x0.2, so g(x) has a scale factor of 0.2 to f(x), and it is stretched horizontally.