Key takeaway: This algebra 1 building functions quiz poses ten choice items on rules, profit, inverses and sequences. It aims at the F-BF and F-LE standards, and every choice has a short rationale.
Try the item by hand before you read the options.
Answer these 10 multiple-choice questions on writing functions from situations, combining functions, inverses of linear functions and constant rates of change. Each question has exactly one correct answer. Check your choice by substituting values.
The diagram shows the steps of a function. Which expression matches it?
Revenue is \(R(x)=9x\) and cost is \(C(x)=4x+75\). Which expression is the profit \(P(x)\)?
For \(R(x)=9x\) and \(C(x)=4x+75\), how many units give break-even?
Let \(f(x)=7x+2\) and \(g(x)=3x-5\). What is \((f-g)(x)\)?
Let \(f(x)=4x+9\). Solve \(f(x)=33\).
Let \(f(x)=3x-12\). Which expression gives \(x\) in terms of \(y\)?
Which statement is true for the table?
A sequence has \(a(0)=20\) and \(a(n)=a(n-1)+7\). Which explicit rule matches it?
The point \((2,7)\) is on the graph of \(f\). Which point is on the graph of its inverse?
A skate park charges $5 to enter plus $3 per hour, so \(T(h)=3h+5\). Aisha paid $23. How many hours did she skate?
🎉 Quiz complete!
Remember:
- Standards F-BF.A.1a, F-BF.A.1b, F-BF.B.4a and F-LE.A.1b: write functions from contexts, combine them, find simple inverses and spot constant rates.
- Explicit \(f(h)=8h+12\) and recursive \(f(0)=12,\ f(h)=f(h-1)+8\) describe the same situation.
- Profit equals revenue minus cost: \(P(x)=R(x)-C(x)\); break-even is where \(P(x)=0\).
- To invert \(y=2x+3\), solve for \(x\): \(x=\frac{y-3}{2}\).
- A constant rate of change means equal input steps give equal output changes.
What does the algebra 1 building functions quiz cover?
The first item turns the steps multiply by 5, then subtract 2 into \(f(x)=5x-2\). Next, revenue \(9x\) and cost \(4x+75\) give profit \(5x-75\), and break-even happens at 15 units. Subtracting \(3x-5\) from \(7x+2\) gives \(4x+7\).
How do you handle inverses and sequences?
To solve \(4x+9=33\), subtract 9 and divide by 4, so \(x=6\). For \(f(x)=3x-12\), the expression for x is \(\frac{y+12}{3}\). A sequence that starts at 20 and adds 7 has the explicit rule \(a(n)=7n+20\).
- A point \((2,7)\) on f means \((7,2)\) lies on the inverse.
- A skate park with \(T(h)=3h+5\) charges $23 for 6 hours.
What does this result suggest you review?
Group the wrong picks by rule, inverse or sequence. Weak inverse picks call for undoing steps backward, while weak profit picks call for subtracting the entire cost.
Where should you go after this building functions quiz?
Retry the missed items and test each rule with a second input. Later, work the worksheet, which adds taxis, tanks and savings. When your checks agree every time, try the printable test.
See every chapter on the Algebra 1 math page.
