Answer:
(a) -1
(b) 4
(c) 14
(d) 61
Step-by-step explanation:
A piecewise function is a function which has <u>different definitions</u> for <u>different intervals</u> of x.
Given:

f(x) has 2 definitions:
Definition 1
when x is <u>more than or equal to -5</u> and <u>less than or equal to 3</u>. This is a <u>linear function</u>.
Definition 2
when x is <u>more than 3</u> and <u>less than or equal to 4</u>. This is a <u>cubic function</u>.
<u>Part (a)</u>
We have to find f(0), so when x = 0.
x = 0 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

Substitute x = 0 in this definition:

<u>Part (b)</u>
We have to find f(1), so when x = 1.
x = 1 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

Substitute x = 1 in this definition:

<u>Part (c)</u>
We have to find f(3), so when x = 3.
x = 3 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

Substitute x = 3 in this definition:

<u>Part (d)</u>
We have to find f(4), so when x = 4.
x = 4 satisfies the condition 3 < x ≤ 4 so the corresponding function is

Substitute x = 4 in this definition:
