Question

Describe how the graph of the function g(x) is related to the parent function f(x), where f(x) = ?

A) Multiplying the function by -3 reflects the parent graph across the x-axis and stretches it horizontally.
B) Multiplying the function by -3 reflects the parent graph across the y-axis and stretches it vertically.
C) Multiplying the function by -3 reflects the parent graph across the x-axis and stretches it vertically.
D) Multiplying the function by -3 reflects the parent graph across the y-axis and stretches it horizontally.

Answer 1

The correct relationship is option C, where the parent function f(x), when multiplied by -3, is reflected across the x-axis and stretched vertically.

Step-by-step explanation:

When we multiply a parent function f(x) by a negative value, in this case, -3, two transformations occur:

• The graph is reflected across the x-axis. Multiplying by a negative value flips the graph upside down.
• The graph is stretched vertically by a factor of 3. This means that for every point on the parent function, its distance from the x-axis is now tripled.

Therefore, the correct relationship between g(x) and the parent function f(x), when f(x) is multiplied by -3, is illustrated by option C: Multiplying the function by -3 reflects the parent graph across the x-axis and stretches it vertically. This affects the slope and y-intercept of the graph in terms of the algebra of straight lines. The slope would become -3 times steeper, and the y-intercept, if positive, would now be negative, but also multiplied by 3 in its absolute value.