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This printable supports Common Core Mathematics Standard HSF-IF.B.4

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# Identifying Key Features of Functions (Grades 11-12)

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## Identifying Key Features of Functions

1.
Given the graph below of the function $f(x) = 2^x$, what is the end behavior as $x -> -oo ?$ Assume 1 unit intervals for both axes.
1. $f(x) -> -oo$
2. $f(x) -> 0$
3. $f(x) -> -1$
4. $f(x) -> oo$
2.
Given the graph of the function $f(x) = log(x)$, for what values of x is the function positive? Assume 1 unit intervals for both axes.
1. $-oo < x < oo$
2. $0 < x < 1$
3. $x>1$
4. $x > 0$
3.
For the absolute value function shown below, where is the function decreasing? Assume 1 unit intervals for both axes.
1. The function is never decreasing.
2. For all values of x.
3. $x>0$
4. $x<0$
4.
The following table lists some values for a function, $f(x)$. What conclusion can be reached about this function from these function values?

 $\ \ \ \ \mathbf{x} \ \ \ \$ $\ \ \ \ \mathbf{f(x)} \ \ \ \$ $-1.5$ $1.38$ $-1.25$ $2.64$ $-1$ $3$ $-0.75$ $2.73$ $-.5$ $2.13$
1. The function is positive for $-oo < x < 0$.
2. The function is increasing for $-oo < x < -1$.
3. The function is positive for all values of x.
4. The function has a relative maximum near $x=-1$.
5.
Given the table for certain values of a function, $f(x)$, which of the following is most likely a feature of this function?

 $\ \ \ \ \mathbf{x} \ \ \ \$ $\ \ \ \ \mathbf{f(x)} \ \ \ \$ $-3$ $-27$ $-2$ $-8$ $-1$ $-1$ $0$ $0$ $1$ $1$ $2$ $8$ $3$ $27$
1. It has odd symmetry.
2. It is decreasing on $-oo < x < 0$.
3. The value of the function approaches 0 as $x-> oo$.
4. There is a relative minimum at $x= -3$.
6.
The table below gives some of the values of a function, $f(x)$. Which of the following is most likely true, using only the data from the table?

 $\ \ \ \ \mathbf{x} \ \ \ \$ $\ \ \ \ \mathbf{f(x)} \ \ \ \$ $-0.5$ $1.03$ $0$ $2$ $0.5$ $1.03$ $1$ $-1.5$ $1.5$ $-4.47$ $2$ $-7$ $2.5$ $-3.47$
1. The function is negative on the interval $(0,2)$
2. The function is decreasing on the interval $(0,oo)$.
3. The function is decreasing on the interval $(0,2)$
4. The function is positive on the interval $(-oo,0)$.
7.
Given the function $f(x) = x^2 - 2x - 3$, for what interval(s) is $f(x) > 0 ?$
1. $(-1,3)$
2. $(-oo,-1) uu (3,oo)$
3. $(-oo , 0)$
4. $(-oo, oo)$
8.
For the function $f(x) = -x^2 - 4$, for what interval(s) is $f(x) < 0 ?$
1. $(-oo,-2) uu (2,oo)$
2. $(-2,2)$
3. $(-oo,oo)$
4. $(0,oo)$
9.
At what interval is slope of the function $y=(x+2)^2$ positive?
1. $x<0$
2. $x>0$
3. $x> -2$
4. $x<2$
10.
At what interval is slope of the function $y=-(x-2)^2$ positive?
1. $x<0$
2. $x>0$
3. $x> -2$
4. $x<2$
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