Key takeaway: This algebra 1 building functions test has nine questions that cover rules, combinations and inverses. It checks the F-BF and F-LE standards, and the scoring notes sit on a separate page.
Show each substitution, because the key credits method as well as the answer.
This test has 9 questions worth 20 points in total and takes about 45 minutes. Write functions, combine them, find inverses of linear functions and interpret tables. Show every step, and include units in answers to word problems. No calculator is needed.
- Grade: Algebra 1
- Chapter: Building Functions and Inverses
- Common Core: F-BF.A.1a, F-BF.A.1b, F-BF.B.4a, F-LE.A.1b
- Time: 45 minutes
- Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 3 pts; Question 5: 2 pts; Question 6: 3 pts; Question 7: 3 pts; Question 8: 2 pts; Question 9: 1 pt)
Algebra 1 Building Functions Test: questions 1–5
1. Build from a situation (2 points)
Jamal rents a bike with a $10 helmet fee plus $6 per hour.
- Write an explicit function \(f(h)\) for the cost of \(h\) hours. (1 point)
- Write a recursive rule for the same cost. (1 point)
2. Steps of a function (2 points)
The diagram shows the steps that define a function \(g\).
- Write \(g(x)\) as an expression. (1 point)
- Find \(g(9)\). (1 point)
3. Combine functions (2 points)
Let \(f(x)=4x+1\) and \(g(x)=x-6\).
- Write \((f+g)(x)\). (1 point)
- Write \((f-g)(x)\) and find \((f-g)(3)\). (1 point)
4. T-shirt profit (3 points)
The art club sells T-shirts. The graph shows revenue \(R(x)=12x\) and cost \(C(x)=5x+140\) in dollars for \(x\) shirts.
- Write the profit function \(P(x)\). (1 point)
- Find the number of shirts needed to break even. (1 point)
- Find the profit for 35 shirts. (1 point)
5. Solve f(x) = c (2 points)
Let \(f(x)=-3x+14\).
- Solve \(f(x)=5\). (1 point)
- Solve \(f(x)=-7\). (1 point)
Algebra 1 Building Functions Test: questions 6–9
6. Inverse of a linear function (3 points)
Let \(f(x)=\frac{2}{3}x+4\).
- Write an expression for the inverse, giving \(x\) in terms of \(y\). (2 points)
- Use it to find the input when the output is 10. (1 point)
7. Water tank (3 points)
A water tank holds 150 gallons at time 0 and drains at 6 gallons per minute, so the water left is \(W(t)=150-6t\).
- Find the time when 90 gallons are left. (1 point)
- Write \(t\) in terms of \(W\). (1 point)
- Find the time when the tank is empty. (1 point)
8. Constant rate in a table (2 points)
Mei says the table shows a constant rate of change.
- Decide whether Mei is correct and justify the answer. (1 point)
- State the rate of change of \(y\) per 1 unit of \(x\). (1 point)
9. Check an inverse (1 point)
Let \(f(x)=2x+3\) and \(g(x)=\frac{x-3}{2}\). Find \(g(f(5))\) and state what it shows.
What does the algebra 1 building functions test ask?
Jamal’s bike rental opens the test with a $10 helmet fee plus $6 per hour. Next, a diagram defines a function through steps. Then you combine \(f(x)=4x+1\) with \(g(x)=x-6\), and you compute a difference at 3.
A T-shirt graph shows revenue \(R(x)=12x\) and cost \(C(x)=5x+140\), so you find the break-even point and write profit.
How should you prepare for this test?
Practice solving \(f(x)=c\) with negative slopes, such as \(-3x+14=5\). Next, rewrite \(f(x)=\frac{2}{3}x+4\) for x in terms of y. Finally, compose \(g(f(5))\) for \(f(x)=2x+3\) to confirm an inverse.
- The water tank follows \(W(t)=150-6t\).
- The table question asks you to judge Mei’s constant-rate claim.
How do you justify a constant rate?
List the changes in y for equal changes in x. If all changes match, the rate is constant. Because the key rewards the comparison, show the list.
What should you do after the building functions test?
Match your paper to the key and flag each step that lost credit. Then rewrite the inverse question with a different fraction. If the water tank cost points, practice reading what the intercept and the slope mean.
See every chapter on the Algebra 1 math page.
