These 23 problems practice the core ideas of F-IF.A.1, F-IF.A.2 and F-IF.B.5. You will decide when a relation is a function, evaluate functions written with function notation, and state the domain and range from equations, tables, graphs and stories.
Early problems are short and visual. The last six are word problems that ask you to interpret outputs such as \(f(a)=b\) and to choose sensible domains.
Problem 1: Function from ordered pairs
Decide whether the relation \(\{(1,4),(2,7),(3,10),(4,13)\}\) is a function. Explain.
Problem 2: Repeated input
Decide whether \(\{(2,5),(3,8),(2,9),(4,1)\}\) is a function. Explain.
Problem 3: Mapping diagram
Does the mapping diagram show a function? Explain.
Problem 4: Function from a table
Does the table define \(y\) as a function of \(x\)? Explain.
Problem 5: Vertical line test: curve
Use the vertical line test to decide whether the graph shows a function.
Problem 6: Vertical line test: V shape
Use the vertical line test to decide whether the graph shows a function.
Problem 7: Evaluate a linear function
Let \(f(x)=3x-5\). Find \(f(4)\), \(f(-2)\) and \(f(0)\).
Problem 8: Evaluate a quadratic function
Let \(g(x)=x^{2}+2x-8\). Find \(g(3)\), \(g(-4)\) and \(g(0)\).
Problem 9: Evaluate an absolute value function
Let \(h(x)=|x-4|+3\). Find \(h(1)\), \(h(4)\) and \(h(9)\).
Problem 10: Negative and fractional inputs
Let \(k(x)=-2x^{2}+5x\). Find \(k(-3)\) and \(k(\frac{1}{2})\).
Problem 11: Find the input
Let \(f(x)=2x+7\). Find \(x\) when \(f(x)=19\), and find \(x\) when \(f(x)=-5\).
Problem 12: Read a function table
The table gives some values of a function \(f\). Find \(f(2)\), find \(f(-1)\), and find every \(x\) with \(f(x)=3\).
Problem 13: Read a function graph
Use the graph to find \(f(0)\), \(f(4)\), and all \(x\) with \(f(x)=0\).
Problem 14: Input with a variable
Let \(f(x)=3x-2\). Write simplified expressions for \(f(a+1)\) and \(f(2a)\).
Problem 15: Domain and range of a segment
State the domain and range of the function shown. Use inequalities.
Problem 16: Domain and range of a parabola
State the domain and range of the function whose graph is shown.
Problem 17: Cupcake sale (discrete)
At a bake sale, cupcakes cost \(\$3\) each. A customer may buy 1 to 6 cupcakes. The cost is \(C(n)=3n\). State the domain and range, and tell whether the situation is discrete or continuous.
Problem 18: Birthday relation
In a class, each student is paired with his or her birthday. Is this relation a function from students to birthdays? Is the reverse relation, birthdays to students, a function? Explain.
Problem 19: Plumber charges
A plumber charges \(C(h)=25h+40\) dollars for a job that takes \(h\) hours. Explain what \(C(3)=115\) means, then find \(C(2.5)\).
Problem 20: Height of a tossed ball
The height of a ball in feet, \(t\) seconds after it is tossed, is \(h(t)=-16t^{2}+48t+4\). Explain what \(h(2)=36\) means, and find \(h(1.5)\).
Problem 21: Filling a tank (continuous)
An empty tank holds 40 gallons. It fills at 5 gallons per minute until it is full, so \(V(t)=5t\). State the domain and range, and tell whether the situation is discrete or continuous.
Problem 22: Taxi fare
A taxi fare is \(F(m)=2.50+1.75m\) dollars for a ride of \(m\) miles. Find \(F(6)\). Then find the distance of a ride that costs \(\$20.00\).
Problem 23: Garden area
Sofia has 40 feet of fence for a rectangular garden. If the width is \(w\) feet, the length is \(20-w\) feet, and the area is \(A(w)=w(20-w)\) square feet. Find \(A(8)\). Find the widths with area \(75\text{ ft}^{2}\). State a reasonable domain and range.
See every chapter on the Algebra 1 math page.