Question

Find ℎ(−5) when ℎ(x) = −3|x − 1| + 4

Answer 1

ℎ(−5) is −14.

Explanation:

To find the value of ℎ(−5), we plug −5 in for x in the expression for ℎ(x):

ℎ(−5) = −3|−5 − 1| + 4

To evaluate the absolute value, we need to find the distance between −5 and 1 on the number line. Since the absolute value function is always non-negative, the distance between −5 and 1 will be positive.

To find the distance between −5 and 1, we subtract the smaller number from the larger number:

|−5 − 1| = |−6| = 6

Now we can plug this value into the expression for ℎ(−5) to find its value:

ℎ(−5) = −3 * 6 + 4

ℎ(−5) = −18 + 4

ℎ(−5) = −14

Therefore, the value of ℎ(−5) is −14.