The graph of the cube root parent function y =∛ x is translated to form f(x) shown on the graph.
2 answers:
1. draw the graph of the parent function ![y= \sqrt[3]{x}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%5B3%5D%7Bx%7D%20)
, as shown in the attached figure.
a few important point will be enough: (0, 0), (1, 1), (-1, -1), (8, 2), (-8, -2)
2. (0, 0) is an important point of the parent function, because as we go from the left to the right, the graph is concave up, than at (0, 0) it switches to concave down.
this point is called an inflection point, and in this function there is clearly only one.
3. The inflection point (0, 0) of the parent function has been translated to (-6, 1), so all points have been shifted 6 units left and one unit up
so![f(x)= \sqrt[3]{x+6}+1](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Csqrt%5B3%5D%7Bx%2B6%7D%2B1%20)
Answer: A
Remark, for horizontal shift, we use the opposite sign, for vertical shift, the same sign
a few important point will be enough: (0, 0), (1, 1), (-1, -1), (8, 2), (-8, -2)
2. (0, 0) is an important point of the parent function, because as we go from the left to the right, the graph is concave up, than at (0, 0) it switches to concave down.
this point is called an inflection point, and in this function there is clearly only one.
3. The inflection point (0, 0) of the parent function has been translated to (-6, 1), so all points have been shifted 6 units left and one unit up
so
Answer: A
Remark, for horizontal shift, we use the opposite sign, for vertical shift, the same sign
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