Evaluating and Solving from Tables and Graphs

Work each one out before you check it. Every question has a scratch pad and a calculator.

1. Question 1

   The function $f$ is given by the table

   $$\begin{array}{c|cccccc} x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline f(x) & 1 & 4 & -1 & 3 & 0 & -2 \end{array}$$

   Evaluate $f(3)$, and solve $f(x) = 3$.

   $f(3) =$

   $f(x) = 3$ when $x =$

   Check

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2. Question 2

   The function $g$ is given by the table

   $$\begin{array}{c|cccccc} x & -3 & -1 & 0 & 2 & 4 & 5 \\ \hline g(x) & 2 & 6 & -3 & 4 & 6 & -1 \end{array}$$

   Solve $g(x) = 6$.

   smaller solution: $x =$

   larger solution: $x =$

   Check

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3. Question 3

   The graph of $f$ consists of two straight segments: one from $(-4, 1)$ to $(0, 5)$, and one from $(0, 5)$ to $(6, -1)$. Evaluate $f(4)$.

   $f(4) =$

   Check

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4. Question 4

   The graph of $f$ consists only of three straight segments: from $(-5, -3)$ to $(-3, 1)$, from $(-3, 1)$ to $(0, -2)$, and from $(0, -2)$ to $(2, 2)$. Solve $f(x) = 0$: how many solutions are there, and what is the largest?

   number of solutions:

   largest solution: $x =$

   Check

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5. Question 5

   The graph of $g$ is V-shaped, made of two straight segments: from $(-3, 4)$ to $(1, -4)$, and from $(1, -4)$ to $(5, 4)$. Find $g(0)$, then find the other input $x \neq 0$ with $g(x) = g(0)$.

   $g(0) =$

   other input: $x =$

   Check

   Scratch padCalculator