Question

Let f(x)=−9x+1. Match the function with the description.

The graph of g is a reflection in the y-axis of the graph of f.
The graph of g is a reflection in the x-axis of the graph of f.
The graph of g is a horizontal translation 16 units right of the graph of f.
The graph of g is a vertical translation 16 units down of the graph of f.

Answer 1

The four transformations of function f(x) = -9x + 1 are represented as g(x) = 9x + 1 for reflection in the y-axis, g(x) = 9x - 1 for reflection in the x-axis, g(x) = -9x + 145 for a horizontal translation 16 units to the right, and g(x) = -9x - 15 for a vertical translation 16 units down.

Step-by-step explanation:

To match the function f(x) = -9x + 1 with the correct description of the graph of a new function g, we should understand how transformations affect the graph of a function. Let's go through the given descriptions one by one.

Reflection in the y-axis would change the sign of the x-coefficient, turning our function into g(x) = 9x + 1. Reflection in the x-axis would change the sign of the entire function, turning our function into g(x) = 9x - 1. A horizontal translation 16 units right would add 16 to the x-value, resulting in g(x) = -9(x-16) + 1 or g(x) = -9x + 145 after simplifying. Lastly, a vertical translation 16 units down would subtract 16 from the function value, resulting in g(x) = -9x - 15.