Answered

IDNLearn.com provides a comprehensive platform for finding accurate answers. Receive prompt and accurate responses to your questions from our community of knowledgeable professionals ready to assist you at any time.

Select the correct answer.

Which statement is true about the effects of the transformations on the graph of function [tex]\( f \)[/tex] to obtain the graph of function [tex]\( g \)[/tex]? [tex]\( g(x) = f(x-3) + 4 \)[/tex]

A. The graph of function [tex]\( f \)[/tex] is shifted right 3 units and up 4 units.
B. The graph of function [tex]\( f \)[/tex] is shifted right 3 units and down 4 units.
C. The graph of function [tex]\( f \)[/tex] is shifted left 3 units and down 4 units.
D. The graph of function [tex]\( f \)[/tex] is shifted left 3 units and up 4 units.

Sagot :

GinnyAnsweridn
Let's analyze the given function transformation step-by-step to determine the correct statement about the effects on the graph of function [tex]\( f \)[/tex] to obtain the graph of [tex]\( g \)[/tex].

The given transformation is [tex]\( g(x) = f(x - 3) + 4 \)[/tex].

### Step 1: Horizontal Shift
The term [tex]\( x - 3 \)[/tex] inside the function [tex]\( f \)[/tex]:

1. The expression [tex]\( f(x - h) \)[/tex] indicates a horizontal shift of the graph of [tex]\( f(x) \)[/tex].
2. If [tex]\( h \)[/tex] is positive (i.e., [tex]\( f(x - 3) \)[/tex]), it means the graph of [tex]\( f \)[/tex] is shifted to the right by [tex]\( h \)[/tex] units.
3. Thus, [tex]\( x - 3 \)[/tex] represents a horizontal shift to the right by 3 units.

### Step 2: Vertical Shift
The term [tex]\( + 4 \)[/tex] outside the function [tex]\( f \)[/tex]:

1. The expression [tex]\( f(x) + k \)[/tex] indicates a vertical shift of the graph of [tex]\( f(x) \)[/tex].
2. If [tex]\( k \)[/tex] is positive (i.e., [tex]\( +4 \)[/tex]), it means the graph of [tex]\( f \)[/tex] is shifted upwards by [tex]\( k \)[/tex] units.
3. Thus, [tex]\( +4 \)[/tex] represents a vertical shift upwards by 4 units.

### Conclusion
Combining both transformations:

- The graph of the function [tex]\( f \)[/tex] is shifted to the right by 3 units.
- The graph of the function [tex]\( f \)[/tex] is shifted up by 4 units.

Therefore, the correct statement describing the transformation is:

A. The graph of function [tex]\( f \)[/tex] is shifted right 3 units and up 4 units.

This is the true statement based on the given transformations.
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is your go-to source for accurate answers. Thanks for stopping by, and come back for more helpful information.