Explain how to use the vertex and the value of a to determine the range of an absolute value function.

Explanation:

An absolute value function in the form ...

  f(x) = a|x -h| +k

will have its vertex at (x, y) = (h, k). The sign on scale factor "a" will tell you whether it opens upward (a > 0) or downward (a < 0).

If a is positive, the vertex is a minimum, and the range is [k, ∞).

If a is negative, the vertex is a maximum, and the range is (-∞, k].

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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the function makes a strait line horizontally with no x intercept but a y intercept at 9.