Question

describe how the graph of the function, $f(x + 43)$, is a transformation of the graph of the original function $f(x)$. select one: a. the graph of $f(x + 43)$ is a horizontal shift of 43 units to the right of the graph of $f(x)$. b. the graph of $f(x + 43)$ is a vertical shift of 43 units up of the graph of $f(x)$. c. the graph of $f(x + 43)$ is a horizontal shift of 43 units to the left of the graph of $f(x)$. d. the graph of $f(x + 43)$ is a vertical shift of 43 units down of the graph of $f(x)$.

Explanation:

For function transformations, when we have $f(x + h)$ where $h>0$, the graph of $f(x)$ is shifted horizontally to the left by $h$ units. Here, $h=43$, so $f(x+43)$ is a left horizontal shift of 43 units from $f(x)$.

Answer:

C. The graph of $f(x + 43)$ is a horizontal shift of 43 units to the left of the graph of $f(x)$.