Question
Two quadratic functions are given below.
f(x)=x2
g(x)=x2–5
What transformation can be applied to the graph of f(x) to obtain the graph of g(x)?
Scale the graph of f(x) vertically by a factor of
1
5
.
Scale the graph of f(x) vertically by a factor of 5.
Translate the graph of f(x) 5 units up.
Translate the graph of f(x) 5 units down.
Translate the graph of f(x) 5 units to the left.
Translate the graph of f(x) 5 units to the right.
f(x)=x2
g(x)=x2–5
What transformation can be applied to the graph of f(x) to obtain the graph of g(x)?
Scale the graph of f(x) vertically by a factor of
1
5
.
Scale the graph of f(x) vertically by a factor of 5.
Translate the graph of f(x) 5 units up.
Translate the graph of f(x) 5 units down.
Translate the graph of f(x) 5 units to the left.
Translate the graph of f(x) 5 units to the right.
Answers
GPT-4o mini
To determine the transformation from \( f(x) = x^2 \) to \( g(x) = x^2 - 5 \), we will compare the two functions.
The function \( g(x) = x^2 - 5 \) can be seen as \( f(x) \) with a vertical shift. Specifically, the term \(-5\) signifies that we are moving the graph of \( f(x) \) down by 5 units.
Thus, the correct transformation to apply to the graph of \( f(x) \) to obtain the graph of \( g(x) \) is:
**Translate the graph of \( f(x) \) 5 units down.**
The function \( g(x) = x^2 - 5 \) can be seen as \( f(x) \) with a vertical shift. Specifically, the term \(-5\) signifies that we are moving the graph of \( f(x) \) down by 5 units.
Thus, the correct transformation to apply to the graph of \( f(x) \) to obtain the graph of \( g(x) \) is:
**Translate the graph of \( f(x) \) 5 units down.**