Question

Options for all the three boxes are:neither student, Becky and Laura

Answer 1

The parent cosine function is given to be:

$f(x)=\cos (x)$

The graph of this function is shown below:

Laura's Function:

Laura's function is given to be horizontally compressed by a factor of 1/3 and reflected over the x-axis.

The rule for horizontal compression by a factor of 1/a is given to be:

$f(x)\Rightarrow f(\frac{1}{a}\cdot x)$

and the rule for reflection over the x-axis is given to be:

$f(x)\Rightarrow-f(x)$

Therefore, Laura's function will be:

$f(x)=-\cos (3x)$

The graph of the function will be:

Becky's Function:

Becky's function is given to be:

$f\mleft(x\mright)=3\cos \mleft(x-\pi\mright)$

The graph is given to be:

ANSWERS:

BECKY's GRAPH is the FIRST GRAPH

The SECOND GRAPH belongs to NEITHER

LAURA's GRAPH is the THIRD GRAPH