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5.05 Comparing functions across representations

Adaptive
Worksheet

Interactive practice questions

Parabola $P$P is given by $y=-\frac{\left(x+2\right)^2}{4}-2$y=(x+2)242 and a table of values for parabola $Q$Q is provided below.

Parabola $Q$Q:

$x$x $-1$1 $1$1 $3$3
$y$y $-2$2 $-1$1 $-2$2
a

Graph Parabola $Q$Q below.

Loading Graph...
b

Which function has the greatest maximum?

Parabola $P$P

A

Parabola $Q$Q

B
c

Given that we can obtain parabola $Q$Q by translating parabola $P$P to the right by $3$3 places and up by $1$1 place, how many times do the parabolas intersect?

Once

A

Zero times

B

Twice

C

Three times

D
d

Which function is decreasing on the domain $-2\le x\le1$2x1?

Neither parabola $P$P nor parabola $Q$Q

A

Parabola $P$P and parabola $Q$Q

B

Parabola $P$P

C

Parabola $Q$Q

D
Easy
2min

The parabola $P$P is given by $y=\left(x-5\right)^2+5$y=(x5)2+5 and the parabola $Q$Q is given by $y=-2\left(x-7\right)\left(x-3\right)$y=2(x7)(x3).

Easy
4min

Parabola $P$P is given by $y=\frac{11\left(x-6\right)^2}{36}-6$y=11(x6)2366 and parabola $Q$Q is given by $y=\frac{13\left(x-3\right)^2}{9}-8$y=13(x3)298.

Easy
4min

The exponential function $P$P is given by $y=4\left(3^{-x}\right)$y=4(3x). A table of approximate function values for $Q$Q is given below.

Medium
3min
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Outcomes

M2.F.IF.C.8

Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.*

M2.F.IF.C.8.A

Compare properties of two different functions. Functions may be of different types and/or represented in different ways.

M2.F.IF.C.8.B

Compare properties of the same function on two different intervals or represented in two different ways.

M2.MP1

Make sense of problems and persevere in solving them.

M2.MP2

Reason abstractly and quantitatively.

M2.MP3

Construct viable arguments and critique the reasoning of others.

M2.MP4

Model with mathematics.

M2.MP6

Attend to precision.

M2.MP7

Look for and make use of structure.

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