1. Integrated Math Three – Quarter 1 Benchmark Review

2. Function or not a function? 1,3 2,4 3,−1 (4,4)
Function or not a function? 1,3 2,4 3,3 (1,4)

3. The graph of f(x) is shown below. What is 𝑓 3 +𝑓(1)

4. What is the domain of the function
𝑓 𝑥 = 𝑥−2
What is the domain of the function 𝑓 𝑥 = 𝑥 2
𝑓 𝑥 =4𝑥+2

5. Graph the following equation:
𝑓 𝑥 = log 3 (𝑥−2) +1

6. Graph the following equation: 𝑓 𝑥 = log 2 3𝑥

7. Graph the following equation with domain 𝑥> 0, 𝑓 𝑥 = ( 1 2 𝑥) 𝑥

8. Graph the following equation:
𝑓 𝑥 =2− log 10 (1−𝑥)

9. For the following function fill in the corresponding y-values in the table: 𝑓 𝑥 = log 4 𝑥−2X Y 3 6 18 66

10. 𝑓 𝑥 = 3 3𝑥−1 , 𝑔 𝑥 = 3 2𝑥+5 ,
ℎ 𝑥 =3 𝑒 −4𝑥 , 𝑗 𝑥 = 1 2 𝑒 5𝑥−1
What is 𝑓 𝑥 ∗𝑔 𝑥 ?
What is 𝑓(𝑥) 𝑔(𝑥) ?
What is ℎ 𝑥 ∗𝑗 𝑥 ?
What is ℎ(𝑥) 𝑗(𝑥) ?

11. 𝑓 𝑥 =2 𝑥 2 −3𝑥+10, 𝑔 𝑥 =−3 𝑥 2 +𝑥−15
What is 𝑓 𝑥 +𝑔 𝑥 ?
What is 𝑓 𝑥 −𝑔 𝑥 ?
What is 𝑓 𝑥 ∗𝑔 𝑥 ?
If 𝑓 𝑥 =4𝑥−8, What is 3 𝑓 𝑥 +20?

12. 𝑓 𝑥 =5 𝑥 2 −4𝑥+5, 𝑔 𝑥 =3𝑥+4
What is 𝑓∗𝑔 𝑥 ?
What is 𝑓 𝑔 𝑥 ?
What is 𝑔 𝑓 𝑥 ?

13. 𝑓 𝑥 =5𝑥−2, 𝑔 𝑥 =2 𝑥 2 +7𝑥−10, ℎ 𝑥 =3 𝑥 2 +𝑥−2
Put them in order from least to greatest leading coefficient.
𝑓 𝑥 ∗𝑔(𝑥)
𝑓 𝑥 ∗ℎ(𝑥)
ℎ 𝑥 ∗𝑔(𝑥)
𝑓 𝑥 −𝑔(𝑥)
𝑔 𝑥 −ℎ(𝑥)
ℎ 𝑥 −𝑓 𝑥

14. Find the inverse of 𝑓 𝑥 =2𝑥−3
Find the inverse of 𝑓 𝑥 =2 𝑥 2 −3 𝑓𝑜𝑟 𝑥≥0

15. Find the inverse of 𝑓 𝑥 = 1 2 (𝑥−1) 2 𝑓𝑜𝑟 𝑥>1
Solve: 3= log 2 𝑥

16. Find the inverse of 𝑓 𝑥 = −1 8 𝑥 3
Find the inverse of 𝑓 𝑥 =4( 3 2𝑥 )

17. Graph the following points: 1,2 , 2,3 , 3,6 , 4,11
Graph the following points: 1,2 , 2,3 , 3,6 , 4,11 . 𝑡ℎ𝑒 𝑑𝑜𝑚𝑎𝑖𝑛 𝑖𝑠 𝑥≥1 Write the equation of inverse of this quadratic function.

18. Consider the graph of the function below: What is the value of 𝑓 −1 3 ?
Graph the inverse of the line above on the same grid.

19. Let 𝑓 𝑥 𝑏𝑒 𝑎 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑤𝑖𝑡ℎ 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑓 −1 𝑥
Let 𝑓 𝑥 𝑏𝑒 𝑎 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑤𝑖𝑡ℎ 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑓 −1 𝑥 . The table below shows values of the function for selected values of x in its domain. Based on this table, what is the value of 𝑓 −1 −1 ? X Y -5 -3 -1 2 6 3 7

20. Consider the graph below
Consider the graph below. Restrict the domain so that f(x) does have an inverse.

21. Solve for x: 2 4 𝑥 =512 Show all steps and use definition of log to solve.
Solve for x: 𝑥−1) =500

22. Are the following inverses? Explain
𝑓 𝑥 = 4 𝑥 , 𝑔 𝑥 = 𝑙𝑜𝑔 4 𝑥 Are f and g inverses? Explain
ℎ 𝑥 = 1 3 𝑥+6, 𝑗 𝑥 =3𝑥−6 Are h and j inverses? Explain
𝑘 𝑥 =2 𝑥 2 , 𝑙 𝑥 = 𝑥 2 Are k and l inverses? Explain
𝑚 𝑥 = 𝑥−3 +1, 𝑛 𝑥 = (𝑥−1) 2 +3 Are m and n inverses? Explain