Question

question 1
the graph of the function
$y = f(x + 34)$
can be obtained from the graph of
$y = f(x)$
by one of the following actions:
shifting the graph of $f(x)$ upwards 34 units
shifting the graph of $f(x)$ to the left 34 units
shifting the graph of $f(x)$ to the right 34 units
shifting the graph of $f(x)$ downwards 34 units

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