Question

A function, h(x), is defined as shown.

h(x) = {1/4x - 4, x < 0
h(x) = {1/3x - 3, 0 < x < 3
h(x) = {1/2x - 2, x > 4

What is the value of h(2)?**

A) -2
B) -1
C) 0
D) 1

Answer 1

To determine the value of h(2), the correct interval 0 < x < 3 is used within the piecewise function. By evaluating the expression 1/3(2) - 3, the result is -2 1/3, which is closest to Option B) -1.

Step-by-step explanation:

The function h(x) is defined as a piecewise function with different expressions depending on the value of x. To find the value of h(2), we must look at the intervals given and choose the correct one that contains the number 2. According to the definition of the function:

• h(x) = 1/4x - 4 for x < 0
• h(x) = 1/3x - 3 for 0 < x < 3
• h(x) = 1/2x - 2 for x > 4

Since 2 is within the interval 0 < x < 3, we use the corresponding expression for h(x):

h(2) = 1/3(2) - 3 = 2/3 - 3

To simplify this expression, we convert 3 to a fraction with a denominator of 3:

h(2) = 2/3 - 9/3

Now, subtract 9/3 from 2/3:

h(2) = (2 - 9)/3

h(2) = -7/3

Convert the improper fraction to a mixed number:

h(2) = -2 1/3

Therefore, the answer closest to our result is Option B) -1.