5 exercises · 2 automatically checked · 3 written self-checks · Untimed
2 questions · Shuffled order · Untimed practice
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If f(x) = x2 − 2x, what is f(−2)?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
8. Replace both occurrences of x with (−2): f(−2) = (−2)2 − 2(−2) = 4 + 4 = 8. The input is negative, but the output need not be. Parentheses keep the two negative signs in the product visible. Repair: Example 4.03.
If g(x) = 3x + 1, for what value of x is g(x) = 16?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
5. The given number 16 is an output. Set the rule equal to it: 3x + 1
Review Graph and function foundations
Write your complete response before opening the model answer. Compare both your answer and your reasoning.
A linear function has values L(2) = 9, L(5) = 18, and L(9) = 30. Find its rate of change and a formula for L(x).
Rate 3; L(x)
What is the real domain of h(x) = ?
[1, 4) ∪ (4, ∞). A real square root requires x − 1 ≥ 0, so x ≥ 1. The denominator also requires x − 4 ≠ 0, so x ≠ 4. Both restrictions apply simultaneously. The equivalent verbal description is “all real x ≥ 1, except 4.” Repair: Example 4.11.
A straight graph segment joins a closed point at (−1, 4) to an open point at (3, 0). State its domain and range.
Domain [−1, 3); range (0, 4]. Read the input values from left to right: −1 is included and 3 is excluded. Read the output values from bottom to top: 0 is excluded and 4 is included. The segment contains all intermediate values. A decreasing graph still has its range written in increasing order. Repair: Example 4.12.
Check whether you confused an input with an output, inferred an unstated rule, ignored an endpoint, or used a visual distance instead of an axis value. When an equation is available, verify a graph reading by substitution.
You should move between a rule, table, graph, and context without reversing input and output. Distinguish a function from a one-to-one function: different inputs may share an output. Use a linear model only when the information supports it.