Benchmark 2 Review 2
IF.2
Name_____________________________
Date________________________
1. Evaluate the following expressions given the functions below:
f ( x)  x 2  7
g ( x)  3x  1
h( x)  2 x 2  4 x
a. g(10) =
b. f( - 3) =
c. h(–2) =
d. g ( x)  53 ; x = ____
e. g ( x)  79 ; x = ____
f.
f ( x)  g ( x)
2. Given this graph of the function f(x):
f(x)
5
y
x
-5
5
-5
Find:
a. f (4) 
b. f (2) =
c. f ( x)  2 ; x=____
d. f(x) = 5 ; x=____
3. Determine if the following is a function or not. Write YES or NO for your answer.
a.
Input
1
2
Output
7
-7
8
-8
___________
b.
c.
___________
Input
Output
3
5
7
2
4
6
____________
IF.4
Describe the characteristics of each graph: State the Domain, Range, Interval of Increase and Interval
of Decrease as both Interval Notation and an Inequality
4.
Domain:
Domain:
Range:
Range:
Int, of Incr:
Int, of Incr:
Int. of Decr:
Int, of Decr:
X-Intercept:
Y-Intercept:
__________________________________________________________________________________
5.
Domain:
Domain:
Range:
Range:
Int, of Incr:
Int, of Incr:
Int. of Decr:
Int, of Decr:
X-Intercept:
Y-Intercept:
_______________________________________________________________________________
6.
Domain:
Domain:
Range:
Range:
Int, of Incr:
Int, of Incr:
Int. of Decr:
Int, of Decr:
X-Intercept:
Y-Intercept:
________________________________________________________________________________
7.
Domain:
Domain:
Range:
Range:
Int, of Incr:
Int, of Incr:
Int. of Decr:
Int, of Decr:
X-Intercept:
Y-Intercept:
8. Solve the following exponential equations:
REI.11
a. 54 x  125
b. 2 x3 
1
32
c. 4 2 x3  64
9. Graph the following transformations based on the parent function 𝑓(𝑥) = 4𝑥 .
REI.11 & BF.3
a. 𝑔(𝑥) = 2 ∙ 4𝑥−3
b. ℎ(𝑥) = 4−𝑥 + 3
1
c. 𝑖(𝑥) = −43𝑥+2 − 5
10. Describe the transformations that are occurring to the parent function 𝑓(𝑥) = 𝑥 2 in the following
equations.
BF.3
a. 𝑔(𝑥) = (𝑥 + 2)2 − 3
b. ℎ(𝑥) = 3 ∙ (−𝑥)2
c. 𝑗(𝑥) = −(𝑥 − 3)2 + 2
11. List the differences between the following two graphs:
a. 𝑓(𝑥) = 𝑥 2 + 1 and 𝑔(𝑥) = (𝑥 + 2)2 + 1
1
b. 𝑓(𝑥) = 2 ∙ 3𝑥 and 𝑔(𝑥) = − 2 ∙ 3𝑥+1
c. 𝑓(𝑥) = −𝑥 and 𝑔(𝑥) = −𝑥 − 3
d. 𝑓(𝑥) = −2𝑥 and 𝑔(𝑥) = −22𝑥 + 5
12. Use the parent function 𝑓(𝑥) = 3𝑥 to write an equation with the following transformations:
a. Reflection over the y-axis and a vertical shrink by a factor of 4
b. Vertical shift down 2 and a horizontal shift to the left 6
c. Refection over the x-axis and a vertical stretch by a factor of 2
d. Horizontal shrink by a factor of 5 and a horizontal shift to the right 3
BF.1
13. Find the following combinations if:
𝑓(𝑥) = 2𝑥 + 1
𝑔(𝑥) = 2𝑥
a. f(x) + g(x)
ℎ(𝑥) = 2𝑥 2 − 3𝑥 + 4
b. 2 ∙ 𝑓(𝑥) − ℎ(𝑥)
𝑗(𝑥) = 3𝑥
c.
𝑓(𝑥)∙𝑗(𝑥)
𝑔(𝑥)
d. the sum of f(x) and h(x) when x = 2
e. the difference of f(x) and j(x) when x = 1
f. the product of g(x) and h(x) when x = -2
IF.6
14. Find the average rate of change for the following:
a. 𝑓(𝑥) = 𝑥 3 − 2𝑥 2 + 6𝑥 − 5 over the interval [2, 6]
b. 𝑓(𝑥) = 25(1.25)𝑥 over the interval [0, 5]
15. During a recent snowstorm, Jimmy measured the total snowfall accumulated at the end of each
hour. He recorded his results in the table below.
What is the approximate average rate of change of the snowfall
a) between 3 p.m. and 5 p.m.?
b) between 1 p.m. and 4 p.m.?
16. The graph shows the relationship between two variables.
What is the value for the average rate of change over the
interval
a) [0, 4]
b) [1, 6]
c) [4, 6]
17. What does it mean to have a constant rate of change? Draw an example.