# 1.07 Comparing function types

## Interactive practice questions

A table of values for the function $P$P and for the function $Q$Q are provided below.

 Function $P$P: $x$x $-2$−2 $-1$−1 $0$0 $1$1 $2$2 $y$y $9$9 $6$6 $3$3 $0$0 $-3$−3 Function $Q$Q: $x$x $0$0 $1$1 $2$2 $3$3 $4$4 $y$y $6$6 $3$3 $2$2 $3$3 $6$6
a

Which of the following statements are true?

Function $P$P is a line and function $Q$Q is a parabola.

A

Function $P$P is a parabola and function $Q$Q is a parabola.

B

Function $P$P is a line and function $Q$Q is a line.

C

Function $P$P is a parabola and function $Q$Q is a line.

D

Function $P$P is a line and function $Q$Q is a parabola.

A

Function $P$P is a parabola and function $Q$Q is a parabola.

B

Function $P$P is a line and function $Q$Q is a line.

C

Function $P$P is a parabola and function $Q$Q is a line.

D
b

Graph the function $P$P below.

c

Graph the function $Q$Q below.

d

Which of the following statements are true?

As $x$x tends to infinity, function $Q$Q is higher than function $P$P.

A

As $x$x tends to infinity, function $P$P is higher than function $Q$Q.

B

As $x$x tends to infinity, function $Q$Q is higher than function $P$P.

A

As $x$x tends to infinity, function $P$P is higher than function $Q$Q.

B
e

Which of the following statements is true on the domain $x<2$x<2?

Function $P$P is increasing and function $Q$Q is increasing.

A

Function $P$P is decreasing and function $Q$Q is increasing.

B

Function $P$P is decreasing and function $Q$Q is decreasing.

C

Function $P$P is increasing and function $Q$Q is decreasing.

D

Function $P$P is increasing and function $Q$Q is increasing.

A

Function $P$P is decreasing and function $Q$Q is increasing.

B

Function $P$P is decreasing and function $Q$Q is decreasing.

C

Function $P$P is increasing and function $Q$Q is decreasing.

D
Easy
Approx 5 minutes

Consider the line $P$P given by the equation $y=-12+\frac{x}{10}$y=12+x10, and the table of values for parabola $Q$Q.

The graph of the parabola $P$P, given by $y=-3\left(x-2\right)^2-3$y=3(x2)23 is shown below.

The line $P$P is given by $y=-4+\frac{4x}{3}$y=4+4x3 and the parabola $Q$Q is given by $y=-\left(x-1\right)\left(x-4\right)$y=(x1)(x4).

### Outcomes

#### MGSE9-12.F.IF.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).