Graphs of Functions Practice Questions

Complete the table of values for $y = x^2 - 4x + 1$.

Use your table to write down the coordinates of the turning point of the graph of $y = x^2 - 4x + 1$.

Write down the value of $x$ for which the value of $y$ is wrong, and give the correct value of $y$.

Write down the equation of the line of symmetry of the graph of $y = x^2 - 5x + 2$.

In the table below, match each equation with the letter of its graph.

Write down the coordinates of the maximum point of the graph of $y = \sin x$ for $0 \le x \le 360$.

Write down all the solutions of $\sin x = 0$ for $0 \le x \le 360$.

Rahul says there is a value of $x$ for which $\sin x = 1.4$.

Explain why Rahul is wrong.

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

On the grid, draw the graph of $y = x^3 - 3x^2 + 2$ for values of $x$ from $-1$ to $3$.

Use your graph to write down estimates for the solutions of $x^3 - 3x^2 + 2 = 0$.

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

Write down the solutions of $3 + 2x - x^2 = 0$.

By drawing a suitable straight line, use the graph to find estimates for the solutions of $3 + 2x - x^2 = 2$.

One solution of $\cos x = -0.6$ is $x = 126.9^\circ$, correct to 1 decimal place.

Use the symmetry of the graph of $y = \cos x$ to find all the other solutions of $\cos x = -0.6$ in the interval $-360^\circ \le x \le 360^\circ$.

Give your answers correct to 1 decimal place.

Sketch the graph of $y = \tan x$ for $0^\circ \le x \le 360^\circ$.

On your sketch, write down the equations of the two asymptotes.

Given that $\tan 72^\circ = 3.08$, correct to 3 significant figures, write down all the solutions of $\tan x = 3.08$ for $0^\circ \le x \le 720^\circ$.

Find the value of $k$.

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

Explain why the curve $C$ does not cross the $x$-axis.

Complete the table of values for $y = \dfrac{8}{x}$.

Explain why $x = 0$ is not included in the table of values.

Jodie says that the graph of $y = \dfrac{8}{x}$ crosses the $x$-axis once.

Is Jodie correct? Give a reason for your answer.

Use the graph to write down estimates for the roots of $x^2 - 3x - 1 = 0$.

By drawing a suitable straight line on the grid, find estimates for the solutions of $x^2 - 5x + 2 = 0$.

Find the value of $a$ and the value of $b$.

Find the exact value of $y$ when $x = 45$.

Write down the number of solutions of the equation $a\sin x + b = 0$ for $0^\circ \le x \le 720^\circ$.

Find the value of $b$ and the value of $c$.

Find the coordinates of the turning point of the graph.