Translation 5-units up.
Horizonatl compression.
STEP - BY - STEP EXPLANATION
What to find?
The transformation that take the graph of function f to the graph of function g.
Given:
f(x) = x²
g(x) = 1/2 x² + 5
To answer the given question, we first need to take notes of the following points:
• If ,f(x), shifts up m-units, then the new formula of the function is ,f(x) + m
,
• If f(x) shifts n-units downward, then the new formula of the function is, f(x) - n.
,
• If the function is multiply by a fraction, it shows a ,compression, takes place.
,
• If the function is multiply by a whole number, then we say there is a ,stretch,.
From the given points above, observe that the to get a function g, 5 is added to the function. That is; g(x) = f(x) + m which implies f(x) is translated 5 units up.
Also the function is multiplies by a fraction of 1/2.
This implies that there is a horizontal compression.
Therefore, the corrrect options are;
Translation 5-units up.
Horizonatl compression.