Math Problem Statement
Solution
The question asks you to use the graph of the function , which is plotted as a solid line, to sketch the graph of .
The transformation represents a horizontal shift. In this case, the graph of is shifted to the left by 2 units because the inside the function affects the -values, shifting the graph leftward.
Looking at the original graph of , which appears to be a parabola opening upward, the correct transformation would shift this parabola two units to the left.
Now, let's check the options:
- Option A: This graph is shifted right, so it is incorrect.
- Option B: This graph seems to be a leftward shift by 2 units, which looks correct.
- Option C: This graph also appears to be a leftward shift, but it is shifted too far.
- Option D: This graph is shifted right, which is incorrect.
So, the correct choice is Option B.
Would you like more details or have any questions?
Here are 5 related questions:
- What is the effect of on the graph of ?
- How does a vertical shift differ from a horizontal shift in graph transformations?
- What happens if the transformation is instead?
- Can you explain how transformations affect the vertex of a parabola?
- How do you determine the direction of a shift based on the equation?
Tip: Remember that shifts inside the parentheses affect the graph horizontally, while those outside affect it vertically!
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Math Problem Analysis
Mathematical Concepts
Function Transformations
Horizontal Shifts
Graphing
Formulas
g(x) = f(x + c) shifts the graph of f(x) left by c units
Theorems
-
Suitable Grade Level
Grades 8-10