Domain = set of all real numbers
This is because we can plug in any x value without restriction. Note the graph goes on forever toward the left and right directions. We can write [tex](-\infty, \infty)[/tex] as the interval notation to mean "set of all real numbers"
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Range = set of all real numbers
Similar idea to the domain. Any y output is possible which is why the range is any real number. Visually, the graph extends forever upward and downward to reinforce this answer.
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x intercept is exactly [tex]\sqrt[3]{4}[/tex] which is the cube root of 4
x intercept is approximately 1.5874
You can use your calculator to compute 4^(1/3) to get the cube root of 4.
This value is the solution to [tex]0 = -x^3 + 4[/tex]. Notice how I replaced f(x) with 0. All x intercepts happen when y = f(x) is zero. This is where the graph crosses the x axis.
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y intercept is 4 which is where the graph crosses the y axis
Plug in x = 0 and simplify to get 4
[tex]f(x) = -x^3 + 4\\\\f(0) = -(0)^3 + 4\\\\f(0) = 4[/tex]
This backs up what the graph is showing.
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As x approaches positive infinity, y approaches negative infinity
Phrased another way: as you move to the right, the graph goes downhill. Think of it as a roller coaster where the point on the curve is the car going downhill.
