Questions and Answers
What transformation is applied to the parent function to obtain g(x) = |x - 5|?
What is the parent function of g(x) = |x - 5|?
At which point does the function g(x) = |x - 5| achieve its minimum value?
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|?
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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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Description
This quiz focuses on the absolute value function g(x) = |x - 5| and its parent function. You'll explore the transformations applied to the parent function, determine transformation characteristics, and compare it with another function. Graphical representation and minimum value analysis are also included.
