# Piecewise defined function questions and answers

Recent questions in Piecewise-Defined Functions
Piecewise-Defined Functions

### Consider the function $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}-{6}{x}^{{{2}}}-{18}{x}+{9}$$ on the interval [-2,4]. What is the absolute minimum of f(x) on [-2,4]? What is the absolute maximum of f(x) on [-2,4]?

Piecewise-Defined Functions

### Consider the function $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}+{6}{x}^{{{2}}}-{90}{x}+{8},{\left[-{5},{4}\right]}$$ find the absolute minimum value of this function. find the absolute maximum value of this function.

Piecewise-Defined Functions

### Find the absolute maximum and absolute minimum values of f on the given interval. $$\displaystyle{f{{\left({x}\right)}}}={5}+{54}{x}-{2}{x}^{{{3}}},{\left[{0},{4}\right]}$$

Piecewise-Defined Functions

### Find the absolute maximum and absolute minimum values of f on the given interval and state where those values occur: $$\displaystyle{f{{\left({x}\right)}}}={x}^{{{3}}}-{3}{x}^{{{2}}}-{9}{x}+{25},{\left[-{5},{10}\right]}$$

Piecewise-Defined Functions

### Rewrite the following without the absolute value symbols. $$\displaystyle{\left|{y}+{7}\right|}\geq{1}$$ $$\displaystyle{y}\leq-{7}{\quad\text{or}\quad}{y}\leq-{8}$$ $$\displaystyle{y}\geq-{7}{\quad\text{or}\quad}{y}\leq-{8}$$ $$\displaystyle{y}\geq-{7}{\quad\text{or}\quad}{y}\leq-{8}$$ $$\displaystyle{y}\geq-{7}$$ $$\displaystyle{y}\leq-{8}$$

Piecewise-Defined Functions

### Plot the complex number and find the absolute value. $$\displaystyle\sqrt{{-{49}}}$$

Piecewise-Defined Functions

### Plot the complex number $$z = -3 - 4i$$ and find its absolute value.

Piecewise-Defined Functions

### Write each expression without using absolute value symbols. $$|0|$$

Piecewise-Defined Functions

### An absolute value function with a vertex of (4,14) is negative on the interval $$\displaystyle{\left(−\infty,−{2}\right)}$$. On what other interval is the function negative?

Piecewise-Defined Functions

### Find the absolute maximum and absolute minimum values of f on the given interval. $$\displaystyle{f{{\left({x}\right)}}}={5}+{54}{x}-{2}{x}^{{3}},{x}\in{\left[{0},{4}\right]}$$

Piecewise-Defined Functions

### Rewrite expression without absolute value bars. $$\displaystyle{\left|{\sqrt{{5}}-{13}}\right|}$$

Piecewise-Defined Functions

### Given the piecewise function below, select all of the statements that are true. $$f(x)= \left\{-x + 1, x < 0\right\} \left\{-2, x = 0\right\} \left\{x^{2} -1, x > 0\right\}$$ A. $$f(4)=7$$ B. $$f(-1)=2$$ C. $$f(1)=0$$ D. $$f(-2)=0$$

Piecewise-Defined Functions

### Write properties absolute value.

Piecewise-Defined Functions

### Rewrite the expression without using the absolute value symbol. $$\displaystyle{\left|{{3}{x}-{5}}\right|}$$ if $$\displaystyle{x}\ge\frac{{5}}{{3}}$$

Piecewise-Defined Functions

### Find the absolute maximum and absolute minimum values of function on the given interval. $$\displaystyle{f{{\left({x}\right)}}}={5}+{54}{x}-{2}{x}^{{3}},{\left[{0},{4}\right]}$$

Piecewise-Defined Functions

### Solve. Absolute value of $$2x+4$$ is greater than 6

Piecewise-Defined Functions

### Need to calculate:The value of G(0) for the function $$G(x)=\begin{cases}x-5\ \ if\ x \leq -1\\x\ if\ \succ 1 \end{cases}$$

Piecewise-Defined Functions

### Could you explain how to solve the given type of problem. (c)Absolute value equation: $$|2x-5|=7$$

Piecewise-Defined Functions