6) suppose the graph of f is given. describe how the graph of each function can be obtained from the graph…

Explanation:

Step1: Reflection about x - axis

The negative sign in front of $f(x)$ (i.e., $-f(x)$) reflects the graph of $y = f(x)$ about the $x$-axis. For any point $(x,y)$ on the graph of $y = f(x)$, the corresponding point on the graph of $y=-f(x)$ is $(x, - y)$.

Step2: Vertical translation

Adding 5 to $-f(x)$ (i.e., $-f(x)+5$) shifts the graph of $y = - f(x)$ vertically upwards by 5 units. For any point $(x,y)$ on the graph of $y=-f(x)$, the corresponding point on the graph of $y=-f(x)+5$ is $(x,y + 5)$.

Answer:

The graph of $y=-f(x)+5$ can be obtained by first reflecting the graph of $y = f(x)$ about the $x$-axis and then translating the resulting graph vertically upwards by 5 units.