Question
True or False: When the graph of the parent function f(x)=cos x is reflected across the x-axis, its y-intercept changes from y=1 to y= -1. Explain.
Answers
GPT 3.5
True.
When the graph of the parent function f(x) = cos(x) is reflected across the x-axis, it means that every point on the graph will move vertically to the corresponding point on the other side of the x-axis.
The y-intercept of the parent function f(x) = cos(x) is (0, 1), which means that when x=0, y=1.
When the graph is reflected across the x-axis, the y-coordinate of every point will be negated (i.e., multiplied by -1).
So, when the graph is reflected, the y-intercept will change from (0, 1) to (0, -1). This means that when x=0, y=-1.
Therefore, when the graph of the parent function f(x) = cos(x) is reflected across the x-axis, its y-intercept changes from y=1 to y=-1.
When the graph of the parent function f(x) = cos(x) is reflected across the x-axis, it means that every point on the graph will move vertically to the corresponding point on the other side of the x-axis.
The y-intercept of the parent function f(x) = cos(x) is (0, 1), which means that when x=0, y=1.
When the graph is reflected across the x-axis, the y-coordinate of every point will be negated (i.e., multiplied by -1).
So, when the graph is reflected, the y-intercept will change from (0, 1) to (0, -1). This means that when x=0, y=-1.
Therefore, when the graph of the parent function f(x) = cos(x) is reflected across the x-axis, its y-intercept changes from y=1 to y=-1.