question 1\nthe graph of the function\n$y = f(x + 34)$\ncan be obtained from the graph of\n$y = f(x)$\nby…

question 1\nthe graph of the function\n$y = f(x + 34)$\ncan be obtained from the graph of\n$y = f(x)$\nby one of the following actions:\nshifting the graph of $f(x)$ upwards 34 units\nshifting the graph of $f(x)$ to the left 34 units\nshifting the graph of $f(x)$ to the right 34 units\nshifting the graph of $f(x)$ downwards 34 units

question 1\nthe graph of the function\n$y = f(x + 34)$\ncan be obtained from the graph of\n$y = f(x)$\nby one of the following actions:\nshifting the graph of $f(x)$ upwards 34 units\nshifting the graph of $f(x)$ to the left 34 units\nshifting the graph of $f(x)$ to the right 34 units\nshifting the graph of $f(x)$ downwards 34 units

Answer

Explanation:

Step1: Recall function transformation rules

For a function (y = f(x + h)), if (h>0), the graph of (y = f(x)) is shifted to the left by (h) units. If (h < 0), the graph of (y = f(x)) is shifted to the right by (|h|) units. Here (h = 34>0).

Step2: Apply the rule to (y=f(x + 34))

When we compare (y = f(x)) and (y=f(x + 34)), according to the rule (y=f(x+h)) (where (h = 34)), the graph of (y = f(x)) is shifted to the left by (34) units.

Answer:

shifting the graph of (f(x)) to the left (34) units