Question

Without graphing, determine the range of the function f(x)=5|x-7|+2

Answer 1

The range of the function is y >= 2

How to determine the range of the function?

The equation of the function is given as:

f(x) = 5|x - 7| + 2

The above function is an absolute value function.

An absolute value function is represented as:

f(x) = a|x -h| + k

Where

Leading coefficient = a

Vertex = (h, k)

This means that

a = 5

(h, k) = (7, 2)

If a is positive, then the vertex is a minimum

This means that the vertex (7, 2) is a minimum

Remove the x value

y = 2

Express as a range

y >= 2

Hence, the range of the function is y >= 2

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