Trigonometry and Functions Practice Questions

Read the following study guide for a concept review:

Trigonometry and Functions Study Guide

Practice Questions

1.	If f(x) = 5x + 2, then to what does 3 relate under function f?
2.	If V(s) = s3, then what is V(4)?
3.	What does the function relate to the number 4?
4.	If f(x) = 10, what is f(17)?
5.	What is s( –1), when s(t) = –16t2 + 4t + 100?
6.	If C(r) = 2πr, then what is C(2.7)?
7.	Evaluate k(2) for k(u) = u3 – 4u2 + 2u – 5.
8.	What is –1 related to under the function q(x) = (x – 5)(x + 1)(x – 4)?
9.	If f(x) = √1 – x2, then what is ?
10.	when , what does p relate to the number –2?
11.	Where does h take the number 10 when h(x) = √x2 – 7x + 4?
12.	What is h( –7), when ?
13.	Evaluate for .
14.	What does do with the number 3?

Find the domain for each of the following functions.

15.
16.	g(x) = 3x4 – 10x
17.	h(x) = √x + 3
18.	y(x) = √5x + 2
19.
20.	g(x) = √4 – x
21.
22.	h(x) = √3 – 4x
23.	g(x) = x3 – √3 – x
24.
25.	The area A of an isosceles right triangle with base and height x is . What is the domain of A?
26.	If a person works t hours on a project that pays $100, then the hourly rate is . What is the domain of r?

Evaluate the following, using the functions h and k defined by:

h(x) = the number of digits to the left of the decimal place in x

k(x) = the number x with every digit 3 replaced by 8

Answers

1.	y(3) = 17, so 3 relates to 17
2.	V(4) = 64
3.	g(4) = 9, so 4 relates to 9
4.	Because the variable x doesn't appear in the formula, there is no place to plug in x = 17. Thus, f(17) = 10.
5.	s(–1) = 80
6.	C(2.7) = 5.4π
7.	k(2) = –9
8.	–1 relates to q( –1) = 0
9.
10.	, so p relates
11.	h(10) = √34, so h takes 10 to √34
12.	h(–7) = –1
13.
14.	, so k takes 3 to
15.	x ≠ –5
16.	the domain of g consists of all real numbers, R
17.	x ≥ –3
18.
19.	x ≠ –2 and x ≠ –4
20.	x ≤ 4
21.	x ≥ –5, except x ≠ 2 and x ≠ –2
22.
23.	x ≤ 3
24.	x ≤ 2, except x ≠ 0,1,–5
25.	While any number can be plugged into , we must consider the fact that x represents the base and height of a triangle. This means that x must be a positive amount. Thus, the domain of this function consists of all positive lengths x > 0.
26.	The domain of r consists of all amounts of time t > 0. Negative amounts of time are impossible.
27.	h(207.32) = 3
28.	h(39.5) = 2
29.	k(3,185) = 8,185
30.	k(l3.843) = 18.848