Consider the graph of the function \\ f(x) = \left| 2 x + 4\right| :
On the same set of axes, graph the function f(x) = 2.
State the number of solutions for the equation \left| 2 x + 4\right| = 2.
Find the solutions to the equation \left| 2 x + 4\right| = 2.
Consider the equation \left| 5 x\right| = 15.
On the same set of axes, graph the functions y = \left| 5 x\right| and y = 15.
Hence, determine the solutions to the equation \left| 5 x\right| = 15.
Consider the graph of the cubic function y = \left(x + 1\right) \left(x - 2\right) \left(x - 3\right).
State the number of solutions to the equation \left(x + 1\right) \left(x - 2\right) \left(x - 3\right) = 0.
Determine the solutions to the equation \left(x + 1\right) \left(x - 2\right) \left(x - 3\right) = 0.
State the number of solutions to the equation \left(x + 1\right) \left(x - 2\right) \left(x - 3\right) = -2.
State the number of solutions to the equation \left(x + 1\right) \left(x - 2\right) \left(x - 3\right) = 6.
Consider the functions y = 9 and y = x^{2}.
Graph the functions on the same coordinate axes.
State the coordinates of the points of intersection.
Hence state the solutions to the equation x^{2} = 9.
For each of the following equations:
Write the equation of the two straight lines that would need to be graphed to find the solution graphically.
Graph the two lines on the same coordinate plane.
Hence, find the value of x that satisfies the two equations simultaneously.
2 x + 2 = - 2 x + 2
\dfrac {x}{3} + \dfrac {1}{3} = - x - 1
To solve for the point(s) of intersection of the hyperbola y = \dfrac{3}{x} and the line y = 5, Laura forms the equation \dfrac{3}{x} = 5.
At how many points will the two graphs intersect?
Solve for the x-coordinate of the point(s) of intersection.
Hence, state the coordinates of the point(s) of intersection.
Consider the function f(x) = \left| 4 x - 4\right|.
Graph the function f(x) on the coordinate plane.
Hence, determine the number of solutions to the equation \left| 4 x - 4\right| = - 2.
The graph of y = 2 x + 6 is displayed:
State the solution of the equation \\ 2 x + 6 = 0.
State the solution of the inequality \\ 2 x + 6 \geq 0.
State the solution of the inequality \\ 2 x + 6 \leq 0.
State the solution of the equation \\ 2 x + 6 = -2.
Consider the following system of equations:
Equation 1: y = - 4 x^{2} + 10 x
Equation 2: y = c
Find the x-intercepts of Equation 1.
Find the axis of symmetry of the graph corresponding to Equation 1.
Hence, determine the coordinates of the vertex for Equation 1.
Graph Equation 1 on the coordinate plane.
For what value of c will there be one solution to the system of equations?
For what values of c will there be two solutions to the system of equations?
The graph of the function y = \left| 4 x + 8\right|+2 is shown:
For what values of c does the equation \left| 4 x + 8\right|+2 = c have two solutions?
For what values of c does the equation \left| 4 x + 8\right|+2 = c have one solution?
For what values of c does the equation \left| 4 x + 8\right|+2 = c have no solutions?
The graphs of the lines \\ y = 17 and y = 4 x - 3 are shown:
Using the graphs, state the solution of the inequality 4 x - 3 < 17.
The graph of the function \\ f \left( x \right) = 2 x^{4} + 3 x^{3} - 7 x^{2} is shown:
Use the graph to determine the values of k for which 2 x^{4} + 3 x^{3} - 7 x^{2} + k = 0 has no solutions.
Write an absolute value equation representing the following:
All numbers x whose distance from 0 is 9 units.
All numbers x whose distance from 4 is 9 units.
If a is a positive number, find the number of solutions for the equation \left|x\right| = a.
Find the value(s) of b so that the equation \left|x\right| = b has only one solution.
Solve each of the following equations:
\left|x\right| = 8
\left|x\right| = - 8
\left|x + 3\right| = 7
\left|1 - x\right| = 3
\dfrac{\left|x\right|}{7} = 6
\left| 2 x\right| - 5 = 4
\left| 3 x + 6\right| = 9
- 3 \left|x + 5\right| = - 9
7 - \left| 4 x\right| = 5
\left| 4 x - 8\right| + 1 = 13
Roxanne performed the following steps to solve the equation 4 \left|x\right| = - 2:
Explain the mistake Roxanne has made in her working.
Determine the correct solution to the equation.
| Step 0: | 4 \left| x \right| = -2 |
|---|---|
| Step 1: | 4x=-2 , 4x=2 |
| Step 2: | x=- \dfrac{1}{2}, x= \dfrac{1}{2} |