In what ways is the graph of g(x) different from the graph of the parent function? Select all that apply.
A. The graph of g(x) is narrower.
B. The graph of g(x) is wider.
C. The graph of g(x) opens downward.
D. The graph of g(x) opens upward.
In what ways is the graph of g(x) different from the graph of the parent function? Select all that apply
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To accurately determine how the graph of g(x) differs from the parent function, we need to analyze the function itself.
Typically, when comparing the transformations of a function to its parent function (like quadratic, cubic, etc.), here is how to interpret the choices:
– A. The graph of g(x) is narrower. (This means it’s a steeper version of the parent function, which could occur if the coefficient of x is greater than 1.)
– B. The graph of g(x) is wider. (This suggests a compression of function, which happens if the coefficient of x is between 0 and 1.)
– C. The graph of g(x) opens downward. (This indicates that if g(x) was to have a negative leading coefficient, it opens downward.)
– D. The graph of g(x) opens upward. (This suggests that g(x) mirrors the upward direction of parent functions like x².)
To select the correct options, you need to know the form of g(x) and whether it represents a transformation (narrower, wider, or direction-based) of its parent function. Generally, if confirming transformations:
– If the leading coefficient is negative, select options C.
– If it is positive, select option D.
– Depending on the value of the leading coefficient, choose A or B accordingly.
If you have the specific function g(x) in mind, you can apply this analysis directly.
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