Graphs of Functions Practice Questions

Complete this table of values for $y = x^2 + 3x$.

$x$	–4	–3	–2	–1	0	1	2
$y$			–2			4

Write down one thing that is wrong with Kofi's graph.

Write down the values of $x$ where the graph crosses the $x$-axis.

Write down the coordinates of the point where the graph crosses the $y$-axis.

$(\quad , \quad)$

Write down the coordinates of the turning point of the graph.

$(\quad , \quad)$

Complete the table of values.

$x$	0.5	1	2	4	5	8
$y$		8		2

On a grid, plot your points and draw the graph of $y = \frac{8}{x}$ for values of $x$ from 0.5 to 8.

Explain why the graph of $y = \frac{8}{x}$ never crosses the $y$-axis.

Write the letter of the correct graph next to each equation.

Equation	Letter
$y = x^3$
$y = 4 - x$
$y = x^2 - 3$
$y = \frac{5}{x}$

Explain how you can tell, from its shape, that graph B is not the graph of a quadratic function.

Complete the table of values for $y = x^2 - 4x + 2$.

$x$	–1	0	1	2	3	4	5
$y$		2			–1

On the grid, draw the graph of $y = x^2 - 4x + 2$ for values of $x$ from –1 to 5.

Write down the coordinates of the turning point of the graph.

$(\quad , \quad)$

Use the graph to find an estimate for the value of $y$ when $x = -1.5$

Use the graph to find the values of $x$ when $y = 1$

Complete the table of values for $y = x^3 - 3x$.

$x$	–2	–1.5	–1	–0.5	0	0.5	1	1.5	2
$y$	–2		2		0		–2		2

On the grid, draw the graph of $y = x^3 - 3x$ for values of $x$ from –2 to 2.

Write down the coordinates of the highest point of your graph for values of $x$ between –2 and 0.

$(\quad , \quad)$

Write down the coordinates of the point where the curve crosses the $y$-axis.

$(\quad , \quad)$

The turning point of the curve is at the point $(3, k)$.

Work out the value of $k$.

Meera says,

"The curve $y = x^2 - 6x + 5$ does not cross the $x$-axis."

Meera is wrong.

Explain why.