To determine which transformation of \( f(x) \) will produce the same graph as \( g(x) \), we need to understand what transformation has been applied to \( f(x) \).
Given functions:
\[ f(x) = 3x \]
\[ g(x) = f(x) + 3 \]
Rewriting \( g(x) \):
\[ g(x) = 3x + 3 \]
We compare \( g(x) \) to \( f(x) \) and see that \( g(x) \) is simply \( f(x) \) shifted upward by 3 units. Therefore, we need to find a transformation that results in shifting \( f(x) \) up by 3 units.
Examining the options:
A. \( h(x) = f(x - 1) \) - This represents a horizontal shift to the right by 1 unit.
B. \( h(x) = f(x) + 1 \) - This represents a vertical shift up by 1 unit.
C. \( h(x) = f(x + 1) \) - This represents a horizontal shift to the left by 1 unit.
D. \( h(x) = 2f(x) \) - This represents a vertical stretch by a factor of 2.
The correct transformation to shift \( f(x) \) up by 3 units is:
\[ h(x) = f(x) + 3 \]
Since \( g(x) = f(x) + 3 \), it appears the question might have a misprint because none of the provided options exactly match \( h(x) = f(x) + 3 \). However, under the assumption the problem intends to find h(x) = f(x) + 3, the correct answer should ideally reflect:
\[ h(x) = f(x) + 3 \]
Though it's not directly provided in the options, for the purpose of selecting the correct answer given what's available:
None of the provided options exactly match \( g(x) = f(x) + 3 \), suggesting a necessary correction in either the provided transformations or reviewing other integrally intended context.
Select the correct answer.
Which transformation of f(x) will produce the same graph as g(x)?
f(x) = 3x
g(x) = f(x) + 3
A.
h(x) = f(x − 1)
B.
h(x) = f(x) + 1
C.
h(x) = f(x + 1)
D.
h(x) = 2f(x)
1 answer