Which transformation of f(x) will produce the same graph as g(x)?f(x) = 3xg(x) = f(x) + 3 A. h(x) = f(x − 1) B. h(x) = 2f(x) C. h(x) = f(x + 1) D. h(x) = f(x) + 1
Question
Which transformation of f(x) will produce the same graph as g(x)?f(x) = 3xg(x) = f(x) + 3 A. h(x) = f(x − 1) B. h(x) = 2f(x) C. h(x) = f(x + 1) D. h(x) = f(x) + 1
Solution
The transformation of f(x) that will produce the same graph as g(x) is D. h(x) = f(x) + 1.
Here's why:
Given f(x) = 3x and g(x) = f(x) + 3, we can substitute f(x) into g(x) to get g(x) = 3x + 3.
Now, let's look at the options:
A. h(x) = f(x − 1) would give us h(x) = 3(x - 1), which simplifies to h(x) = 3x - 3. This is not the same as g(x).
B. h(x) = 2f(x) would give us h(x) = 2 * 3x, which simplifies to h(x) = 6x. This is not the same as g(x).
C. h(x) = f(x + 1) would give us h(x) = 3(x + 1), which simplifies to h(x) = 3x + 3. This is the same as g(x), but it's not one of the options.
D. h(x) = f(x) + 1 would give us h(x) = 3x + 1. This is not the same as g(x).
So, none of the options would produce the same graph as g(x). There seems to be a mistake in the question or the options provided.
Similar Questions
The graph of the parent function, f(x) = x3, is translated such that the function g(x) = (x – 4)3 – 1 represents the new graph. Which transformations occurred? Horizontal translation: Vertical translation:
What kind of transformation converts the graph of f(x)=3|x|+9 into the graph of g(x)=3|x+6|+1?translation 6 units left and 8 units uptranslation 6 units right and 8 units downtranslation 6 units left and 8 units downtranslation 6 units right and 8 units upSubmit
To determine which transformation changes the graph of \( f(x) = x^4 \) to the graph of \( g(x) = (x - 3)^4 - 2 \), we need to understand how transformations affect the graph of a function. 1. **Horizontal Translation**: - \( f(x - h) \) translates the graph of \( f(x) \) to the right by \( h \) units. - \( f(x + h) \) translates the graph of \( f(x) \) to the left by \( h \) units. 2. **Vertical Translation**: - \( f(x) + k \) translates the graph of \( f(x) \) up by \( k \) units. - \( f(x) - k \) translates the graph of \( f(x) \) down by \( k \) units. Given \( g(x) = (x - 3)^4 - 2 \): - The term \( (x - 3) \) indicates a horizontal translation to the right by 3 units. - The term \( -2 \) indicates a vertical translation down by 2 units. So, the correct transformation is: - Translate the graph of \( f(x) = x^4 \) to the right by 3 units. - Then translate it down by 2 units. This matches option **B**: - Translating it to the right by 3 units, then translating it down by 2 units. Therefore, the correct answer is **B**.
Consider the function f(x)=2x.a) Write the equation for the function g(x) obtained by shifting f(x) three units to the up.b) Determine the domain and range of g(x).c) Now, consider h(x)=−2x. Describe the transformation applied to f(x) to obtain h(x).d) Sketch the graphs of f(x), g(x), and h(x) on the same set of axes.
What kind of transformation converts the graph of f(x)=5(x–8)2–1 into the graph of g(x)=5(x–5)2+5?translation 6 units left and 3 units uptranslation 3 units left and 6 units uptranslation 3 units right and 6 units downtranslation 6 units right and 3 units downSubmit
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.