Common Core Standard HSF-IF.C.9 Questions

Grade 11 Functions and Relations CCSS: HSF-IF.C.9

$f(x)$ is the exponential function shown in the following graph, and

$g(x) = 100^x$ , which of the following is true? Assume that the scale of both axes on the graph is one unit.

The y-intercepts are the same.
The y-intercept of $g(x)$ is greater than that of $f(x)$ .
The y-intercept of $f(x)$ is greater than that of $g(x)$ .
The function $g(x)$ has no y-intercept.

Grade 11 Functions and Relations CCSS: HSF-IF.C.9

$f(x) = (x+3)(x-1)(x-2)$ and

$g(x)$ is a polynomial function, some of whose values are given in the table below, which of the following values are zeros of both functions?

$\ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \mathbf{g(x)} \ \ \ \ \ \ \ \ \$
$-6$	$0$
$-5$	$10$
$-4$	$6$
$-3$	$0$
$-2$	$-2$
$-1$	$0$
$0$	$0$
$1$	$-14$
$2$	$-27$

1
0
-3
-6

Grade 11 Functions and Relations CCSS: HSF-IF.C.9

Given the function

$f(x) = 1/10 (x+4)(x+2)(x-1)(x-5)$ , and another polynomial function

$g(x)$ , some of whose values are listed in the following table, which of the statements concerning these two functions is true?

$\ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \mathbf{g(x)} \ \ \ \ \ \ \ \ \$
$-4$	$20$
$-3.5$	$18.5$
$-3$	$15.1$
$-2.5$	$12.2$
$-2$	$14.8$

Both functions have a local minimum on the interval $(-4,-2)$ .
Both functions have a local minimum at $x = -2.$
$f(x)$ has a local minimum on the interval $(-4,-2)$ , and $g(x)$ has a local maximum on this interval.
$g(x)$ has a local minimum on the interval $(-4,-2)$ , and $f(x)$ has a local maximum on this interval.

Grade 11 Functions and Relations CCSS: HSF-IF.C.9

The absolute value function

$f(x)$ is graphed below. Comparing

$f(x)$ to

$g(x) = |3x-1|$ , which of the following statements is true? For the graph, assume that the scale of both axes is one unit.

The minimum value of $f(x)$ is greater than the minimum of $g(x)$ .
The minimum value of $g(x)$ is greater than the minimum of $f(x)$ .
The minimum values of the two functions are equal. But if $f(x_1)$ and $g(x_2)$ are the minimum values, $x_2 > x_1$ .
The minimum values of the two functions are equal. But if $f(x_1)$ and $g(x_2)$ are the minimum values, $x_2 < x_1$ .

Grade 11 Functions and Relations CCSS: HSF-IF.C.9

Let

$f(x) = -1/2 (x-1)(x-3)(x-5)(x-6)$ .

$g(x)$ is also a 4th degree polynomial, some of whose approximate values are listed in the table below. Which statement is certainly true?

$\ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{g(x)} \ \ \ \ \ \ \ \ \ \$
$0$	$-31.8$
$1$	$1.4$
$2$	$3.3$
$3$	$-1.9$
$4$	$-2.5$
$5$	$1.8$
$6$	$-1.2$

Both functions have 2 local maximums and 2 local minimums.
Both functions have 4 distinct zeros.
Both functions have the same range.
$f(x) >= g(x)$ for all values of $x$ .

Grade 11 Functions and Relations CCSS: HSF-IF.C.9

Let

$f(x)$ be the square root function in the following graph. Assume that the scale on both axes is one unit. Also, let

$g(x) = 5*sqrt(-3x - 2) + 2$ . Which of the following statements is true about these functions?

The minimum value of $f(x)$ is less than the minimum value of $g(x)$ .
The minimum value of $g(x)$ is less than the minimum value of $f(x)$ .
The domain of $f(x)$ and the domain of $g(x)$ are identical.
The y-intercepts of both functions are real numbers which are greater than or equal to zero.

Grade 11 Functions and Relations CCSS: HSF-IF.C.9

Let

$f(x)$ be the square root function graphed below. Assume that the scale of both axes is one unit. Let

$g(x) = x^2 - 10x + 24$ . On what interval is

$f(x) > g(x)$ . Round answers to the nearest unit, if necessary.

$(-oo, oo)$
$[0, 3) uu (7,oo)$
$(3, 7)$
$f(x)$ is never greater than $g(x)$ .

Grade 11 Functions and Relations CCSS: HSF-IF.C.9

$f(x)$ is the function in the graph below, and some of the values of the logarithmic function

$g(x)$ are listed in the table below, approximately for what values of

$x$ is

$g(x) > f(x) ?$ For the graph, assume that the scale of both axes is one unit.

Graph - Exponent Function y=2^x

$\ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{g(x)} \ \ \ \ \ \ \ \ \ \$
$-3.75$	$-2.7$
$-3.5$	$-0.9$
$-3.25$	$-0.3$
$-3$	$0.1$
$-2.5$	$0.6$
$-2$	$0.9$
$-1.5$	$1.1$
$-1$	$1.3$
$0$	$1.6$
$1$	$1.9$
$2$	$2.1$
$3$	$2.2$
$4$	$2.4$

$g(x)$ is never greater than $f(x)$ .
$x>1$
$x > -4$
$-3 < x < 1$

Grade 11 Functions and Relations CCSS: HSF-IF.C.9

Let

$f(x)$ be the piecewise function in the graph below. Assume that the scale on both axes is one unit, and that the function is only defined for the values shown in the graph. If

$g(x) = -x^2 + 7x-6$ , for what values of

$x$ , approximately, is

$f(x) > g(x) ?$

$1.5 < x < 5$
$-oo < x < 1.5 " or " 5 < x < oo$
$0 <= x < 1.5 " or " 5 < x <= 10$
$f(x)$ is never greater than $g(x)$ .

Grade 10 Functions and Relations CCSS: HSF-IF.C.9

Given two linear functions,

$f(x)$ which has some of its values listed in the table and

$g(x)$ represented graphically, determine which function has a greater slope. If the slopes are equal, determine whether the lines are coincident or not. Let

$m_f$ represent the slope of function

$f$ and

$m_g$ represent the slope of function

$g$ .

$\ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \$
$-2$	$7$
$-1$	$4$
$0$	$1$
$1$	$-2$
$2$	$-5$

$m_f > m_g$
$m_f < m_g$
$m_f = m_g$ The lines are not coincident.
$m_f = m_g$ The lines are coincident.

Grade 10 Functions and Relations CCSS: HSF-IF.C.9

A company sells coffee mugs. Its cost function is

$C(x) = 1/2 x + 200$ , where

$x$ is the number of coffee mugs sold, and

$C$ is the cost to produce them, in dollars. The table below shows the revenue given the number of coffee mugs sold. With the given data, how many coffee mugs should the company sell in order to make a profit?

$\ \ \ \ \ \ \ \ \ mathbf{"Coffee Mugs Sold"} \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \mathbf{"Revenue"} \ \ \ \ \ \ \ \ \$
$0$	$$0$
$100$	$$206.00$
$200$	$$374.00$
$300$	$$504.00$
$400$	$$596.00$
$500$	$$650.00$
$600$	$$665.00$
$700$	$$644.00$
$800$	$$584.00$

More than zero coffee mugs.
Between 400 and 700 coffee mugs.
Between 200 and 700 coffee mugs.
600 coffee mugs.

Grade 10 Functions and Relations CCSS: HSF-IF.C.9

Shawn's class has been learning about rockets and is planning to launch a small model rocket of their own. The rocket will be launched from ground level, straight up into the air. The rocket does not have a parachute. The class has determined the theoretical height and time of the rocket's flight, as modeled by the following function.

$f(t) = -5t^2 + 100t$

For this function, f(t) is the height of the rocket in meters, and t is the duration of the flight in seconds. When they actually fire the rocket, it lands 18 seconds after it was fired. Shawn was on top of a nearby structure that is 35 meters high. He measured that the rocket, as it ascended, passed him 0.5 seconds after it launched.

Was the theoretical calculation correct, in terms of the maximum height of the rocket? If not, by how much did it over- or underestimate the rocket's maximum height?

The theoretical calculation was correct, the rocket reached a maximum height of 500 m.
The theoretical calculation underestimated the height by 140 m.
The theoretical calculation overestimated the height by 419 m.
The theoretical calculation overestimated the height by 176 m.

Grade 10 Functions and Relations CCSS: HSF-IF.C.9

For what values of

$x$ is the function

$g(x) = -1/2 x^2 + x + 2$ greater than the function shown in the graph below?

For all values of x.
For $-1 < x <2$ .
For $-2 < x < 1$ .
The function $g(x)$ is never greater than the function shown in the graph.

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Common Core Standard HSF-IF.C.9 Questions

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