Question

For the function, tell whether the graph opens up or opens down, identify the vertex, and tell whether the graph is wider, narrower, or the same width as the graph of y = |x|.

y = 2 - |x – 10|

Question 6 options:

opens down, (10, 2), same


opens down, (-10,- 2), narrower


opens down, (-10,- 2), narrower


opens up, (10, 2), same

Answer 1

opens down; (10, 2); same

Explanation:

If the vertex of f(x) is (0, 0) then translating it to (h, k) makes the function look like f(x -h) +k. Changing the sign of f(x) to -f(x) reflects it across the x-axis, so ...

y = 2 - |x -10|

is the function y = |x| reflected across the x-axis and translated 10 units right and 2 units up. Because there is no horizontal or vertical scale factor, the apparent width of the function is the same as the original.