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1.08 Solutions from a graph

Interactive practice questions

The functions $y=-x^3$y=x3 and $y=-4x$y=4x are shown on the graph below.

How many values of $x$x satisfy the equation $-x^3=-4x$x3=4x?

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Easy
< 1min

Consider the functions $f\left(x\right)=-4x+x^2$f(x)=4x+x2 and $g\left(x\right)=-12+6x-x^2$g(x)=12+6xx2.

Medium
5min

Use a graphing calculator to solve $\sqrt[3]{x+13}=2$3x+13=2.

If there is more than one solution, write all of them on the same line, separated by commas.

Medium
1min

Use a graphing calculator to solve $x^{\frac{5}{3}}=5-4x^2$x53=54x2.

Give the solution(s) to the nearest hundredth.

If there is more than one solution, write all of them on the same line, separated by commas.

Medium
2min
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Outcomes

AII-A.REI.11

Given the equations y = f(x) and y = g(x): i) recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x) ii) find the solutions approximately using technology to graph the functions or make tables of values; iii) find the solution of f(x) < g(x) or f(x) ≤ g(x) graphically; and iv) interpret the solution in context. ★

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