0.3/0.5 points details my notes note: type pi for π if needed. enter dne as an answer if a particular…

Explanation:

Step1: Recall secant - function transformation formula

The general form of a secant - function is $y = A\sec(Bt - C)+D$. For the function $f(t)=\sec(2t+\frac{\pi}{4})$, we can rewrite it as $f(t)=\sec(2(t + \frac{\pi}{8}))$. Here $A = 1$, $B = 2$, $C=-\frac{\pi}{4}$, and $D = 0$.

Step2: Determine the horizontal stretch/shrink factor

The horizontal stretch/shrink factor of the graph of $y=\sec t$ to get $y = \sec(Bt)$ is given by $\frac{1}{|B|}$. Since $B = 2$, the graph of $y=\sec t$ is shrunk horizontally by a factor of $\frac{1}{2}$.

Step3: Determine the horizontal shift

For the function $y=\sec(B(t - h))$, the horizontal shift is $h$. For $f(t)=\sec(2(t+\frac{\pi}{8}))$, the shift is $\frac{\pi}{8}$ units to the left.

Answer:

The graph of $f$ is obtained by shrinking the graph of $y = \sec t$ by a factor of $\frac{1}{2}$ and then shifting the graph $\frac{\pi}{8}$ units to the left.