Question

The graph of $f(x)$ is shown below.

For each point $(a,b)$ on the graph of $y = f(x),$ the point $\left( 3a - 1, \frac{b}{2} \right)$ is plotted to form the graph of another function $y = g(x).$ For example, $(0,2)$ lies on the graph of $y = f(x),$ so $(3 \cdot 0 - 1, 2/2) = (-1,1)$ lies on the graph of $y = g(x).$

(a) Plot the graph of $y = g(x).$ Include the diagram in your solution.

(b) Express $g(x)$ in terms of $f(x).$

(c) Describe the transformations that you would apply to the graph of $y = f(x)$ to obtain the graph of $y = g(x).$ For example, one transformation might be to stretch the graph horizontally by a factor of $5.$

Answer 1

Explanation:

ask the message board ! :)

Answer 2

See attached

Explanation:

The graph of both f(x) and g(x) attached

g(x) obtained from f(x) by x→ 3x - 1 and y → y/2 transformation rule

The transformation to get g(x) would be:

• Vertical compression by a factor of 2

• Horizontal shrink by a factor of 3

f(x) is the blue graph

g(x) is the red graph