Task Sets: Compare function properties - Common Core Math - HS Functions

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Recall / Warm-Up

The function $f(x) = -(x-2)^2 + 9$ is in vertex form. What is its maximum value?

$-2$

$2$

$9$

$x = 2$

The table below shows values for $g(x)$ .

$x$	$g(x)$
0	5
1	2
2	1
3	2
4	5

What is the minimum value of $g(x)$ shown in the table?

$0$

$1$

$2$

$x = 2$

The average rate of change of $h(x)$ from $x = 1$ to $x = 4$ is computed as $\frac{h(4) - h(1)}{4 - 1}$ . If $h(1) = 7$ and $h(4) = 16$ , what is the average rate of change?

$9$

$3$

$\frac{16}{7}$

$\frac{7}{16}$

Fluency Practice

Function A (graph): a downward-opening parabola with vertex at approximately $(3, 6)$ and $y$ -intercept at $(0, -3)$ .

Function B (algebraic): $g(x) = -(x - 1)^2 + 8$ .

Which function has the larger maximum value?

Function A, with a maximum of approximately 6.

Function B, with a maximum of 8.

They have equal maxima.

Function A, because it reaches its maximum at $x = 3$ which is farther right.

Function A (algebraic): $f(x) = x^2 - 4$ .

Function B (table):

$x$	$g(x)$
$-3$	$5$
$-1$	$-3$
$0$	$-4$
$1$	$-3$
$3$	$5$

Which function has the larger $y$ -intercept?

Function A, with $y$ -intercept $-4$ .

Function B, with $y$ -intercept $-4$ .

They have equal $y$ -intercepts of $-4$ .

Function A, because $f(x) = x^2 - 4$ has a subtracted $4$ , making it larger.

Function A (table):

$x$	$f(x)$
$0$	$2$
$2$	$6$
$4$	$10$

Function B (algebraic): $g(x) = 3x - 1$ .

Compare the average rates of change of both functions over $[0, 4]$ . Which function has the greater average rate of change?

Function A, with average rate of change $2$ .

Function B, with average rate of change $3$ .

They have equal average rates of change.

They cannot be compared because they are in different representations.

Function A (verbal): "A linear function that starts at 4 when $x = 0$ and increases by 5 for each unit increase in $x$ ."

Function B (algebraic): $g(x) = 6x - 2$ .

What is the $y$ -intercept of Function A minus the $y$ -intercept of Function B? (Compute A's $y$ -intercept minus B's $y$ -intercept.)

Function A (algebraic): $f(x) = x^2 - 6x + 5$ .

Function B (verbal): "A quadratic that opens upward with vertex at $(4, -3)$ ."

Which function has the smaller minimum value?

Function A, with minimum $-4$ .

Function B, with minimum $-3$ .

They have equal minima.

Function A, because it has smaller coefficients.

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Exercises: Compare Function Properties

Recall / Warm-Up

Fluency Practice