Question

Which function is represented by the graph?

Answer 1

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Answer:

  (a)  f(x) = -2|x| + 1

Step-by-step explanation:

Adding a value to a function translates it vertically by that value.

Multiplying a function by a value scales it vertically by that factor. If the factor is negative, a reflection over the x-axis is also involved.

Here, the parent function y=|x| has been reflected over the x-axis, expanded vertically by a factor of 2, and translated upward by 1 unit. This combination of effects is produced by ...

  f(x) = -2|x| +1

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You know the vertical scale factor is 2, because the slopes of the lines have a magnitude of 2. A 1-unit change horizontally gives a 2-unit change vertically.