Worksheet Chapter 8: Graphs of Functions

1. Given $y = x³ - 4x$, calculate $y$ for $x = -1, 0, 2$.

2. Complete the table of values for $y = 2x + 3$ for $x = -1, 0, 1, 2$.

3. True or False: A Many-to-One relation is classified as a function.

4. A linear function is given by $y = mx + c$. (a) If the graph passes through $(0, -5)$ and $(3, 4)$, find the value of $c$ and $m$. (b) Write down the full equation of the function.

5. A quadratic function is defined by $y = x² - 2x - 8$. (a) Calculate the value of $y$ when $x = -2, 1, 4$. (b) Find the roots of the function (x-intercepts where $y = 0$). (c) Determine whether the graph has a minimum or maximum point.

6. The table below shows corresponding values of $x$ and $y$ for $y = 8x$. [x: 1, 2, 4, 8 | y: p, 4, q, 1] (a) Find the values of $p$ and $q$. (b) State the type of graph formed by this function. (c) Find $x$ when $y = 16$.

7. True or False: The graph of $y = -2x² + 5$ has a U-shape curve.

8. Given the function $y = x² - 3x$, find the values of $y$ when $x = -2$ and $x = 3$.

9. Which equation represents a reciprocal function?

10. Fill in the blank: A relation is a function if each element in the domain maps to ________ element in the codomain.