Graph the function `f(x)={(3-x^(2), "if " x lt 1),(x^(3)-4x,"if "x ge 1):}`

Explanation

You can graph this on your graphing calculator . The 2nd TEST command displays an equal sign and five inequality signs. These return the value 1 if an X pixel satisfies the equality or inequality and 0 if it doesn't . For example, `x lt 1` will take the value 1 for pixel values of x that are less than 1 and the value 0 for pixel values of x that are greater than or equal to 1.
Enter `(3-x^(2))(x lt 1) +(x^(3) -4x)(x ge 1)` into `Y_(1)` . For values of x less than `1, (x-1)=1 and (x ge 1)=0`, so for these values only `3-x^(2)` will be grapohed. The reverse is true for values of x greater than I, so only `x^(3) - 4x` will be graphed . This graph is shown on the standard grid in the figure below.

Absolute value functions are a special type of piecewise functions. The absolute value function is defined as `|x|={(x" if "x ge 0),(-x " if " x lt 0):}`
The general absolute value function has the form `f(x) = a|x-h|+k`, with the vertex at (h, k) and shaped like `vee` if `a gt 0` and like `wedge ` if ` a lt 0` . The vertex separates the two branches of the graph, h delineates the domain of all real numbers into two parts. The values are the slopes of the sides a.
The absolute value command is in the MATH/NUM menu of your graphing calculator. You can readily solve absolute value equaions or inequalities by finding of intersection.