Question

Question 6 of 10

How does the graph of f(x) = 3 (4)2-5 + relate to its parent function?
A. The parent function has been stretched.
B. The parent function has been translated up.
C. The parent function has been compressed.
D. The parent function has been translated to the right.

Answer 1

Explanation:

The graph of f(x) = 3 (4)2-5 + is a vertical stretch of the parent function f(x) = 42-5. So the answer is A.

The parent function f(x) = 42-5 is a parabola that opens upwards and has its vertex at (0, -5). The graph of f(x) = 3 (4)2-5 + is also a parabola that opens upwards, but it is taller than the parent function. This is because the factor of 3 in front of the function stretches the parabola vertically by a factor of 3.

The graph of f(x) = 3 (4)2-5 + is also translated upwards by 5 units, since the constant term +5 is added to the function. This means that the vertex of the graph is shifted 5 units upwards, to the point (0, 0).