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Questions and Answers
What transformation is applied to the parent function to obtain g(x) = |x - 5|?
What transformation is applied to the parent function to obtain g(x) = |x - 5|?
- A vertical shift up by 5
- A horizontal shift left by 5
- A vertical reflection over the x-axis
- A horizontal shift right by 5 (correct)
What is the parent function of g(x) = |x - 5|?
What is the parent function of g(x) = |x - 5|?
- g(x) = x^2
- g(x) = x - 5
- g(x) = x + 5
- g(x) = |x| (correct)
At which point does the function g(x) = |x - 5| achieve its minimum value?
At which point does the function g(x) = |x - 5| achieve its minimum value?
- (5, 5)
- (0, 5)
- (5, 0) (correct)
- (0, 0)
Which of the following graphs best represents g(x) = |x - 5|?
Which of the following graphs best represents g(x) = |x - 5|?
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If h(x) = |x + 3|, how does its graph compare to that of g(x) = |x - 5|?
If h(x) = |x + 3|, how does its graph compare to that of g(x) = |x - 5|?
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Study Notes
Transformation of the Parent Function
- The parent function for absolute value is ( f(x) = |x| ).
- The transformation applied to this parent function to obtain ( g(x) = |x - 5| ) is a horizontal shift to the right by 5 units.
Parent Function
- The parent function of ( g(x) = |x - 5| ) is ( f(x) = |x| ).
Minimum Value
- The function ( g(x) = |x - 5| ) achieves its minimum value at ( x = 5 ).
- At this point, the minimum value of ( g(x) ) is ( 0 ) since ( g(5) = |5 - 5| = 0 ).
Graph Representation
- To identify the best graphical representation of ( g(x) = |x - 5| ), look for a V-shaped graph that opens upwards and has its vertex at the point (5, 0).
Comparison with Another Function
- For ( h(x) = |x + 3| ), the graph is transformed by shifting the parent function ( f(x) = |x| ) to the left by 3 units.
- Comparing ( g(x) = |x - 5| ) to ( h(x) = |x + 3| ), the key difference lies in their vertex positions: ( g(x) ) has its vertex at (5, 0), while ( h(x) ) has its vertex at (-3, 0).
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