Functions Worksheet - Math 121: Extra Practice For Test 2 printable pdf download

Functions Worksheet - Math 121: Extra Practice For Test 2

MATH 121: EXTRA PRACTICE FOR TEST 2

Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam.

Linear Functions

1. Consider the functions f (x) = 3x + 5 and g(x) =

2x + 15.

(a) Solve f (x) = 0.

(d) Solve f (x)

g(x).

(e) Graph y = f (x) and y = g(x) and label

(b) Solve f (x) = g(x).

the point that represents the solution to the

equation f (x) = g(x).

2. The cost C, in dollars, of renting a moving truck for a day is given by the function C(x) = 0.25x + 35,

where x is the number of miles driven.

(a) What is the cost if you drive x = 40 miles?

(b) If the cost of renting the moving truck is $80, how many miles did you drive?

that you can drive?

3. A phone company oﬀers a domestic long distance package by charging $5 plus $0.05 per minute.

(a) Write a linear function that relates the cost C, in dollars, of renting the truck to the number x

of miles driven.

(b) What is the cost of renting the truck if the truck is driven 110 miles? 230 miles?

Quadratic Functions

4. Recall that the general form of a quadratic function is f (x) = ax

+ bx + c, where a, b, c are real

numbers and a = 0. Also, the standard form of a quadratic function is f (x) = a(x

+ k, where h

and k are real numbers.

(a) What is the domain of any quadratic function?

(b) What is the name of the graph of any quadratic function?

(d) If a > 0, does the parabola have a maximum or a minimum?

(e) Where does the maximum/minimum of a quadratic function occur?

(f) What is the vertex of the parabola (written in general form, in terms of a, b and c)?

(g) Make sure that you are able to write any quadratic function in standard form.

(h) What is the axis of symmetry of a parabola?

(i) How do you ﬁnd the x intercepts?

(j) What is an alternative way of ﬁnding the location of the vertex of a parabola that has two

x-intercepts (take advantage of symmetry)?

(k) What is the y intercept of a parabola?

(l) True or False: A quadratic function is a polynomial.

Functions Worksheet - Math 121: Extra Practice For Test 2