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10.05 Comparing functions

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

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

Medium
4min

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.

Easy
2min

Consider the functions $f\left(x\right)=2^x$f(x)=2x and $g\left(x\right)=2x^2$g(x)=2x2, for $x\ge0$x0.

Easy
7min
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Outcomes

F.IF.C.9

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

F.BF.A.1

Write a function that describes a relationship between two quantities.

F.BF.A.1.A

Determine an explicit expression, a recursive process, or steps for calculation from a context.

F.LE.A.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

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