Piecewise Definitions of Functions
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- (Video) Piecewise Functions by Eddie Woo Here's a video by Eddie Woo where he explains piecewise functions and how they work. Piecewise Functions A piecewise function is a funct…
By Alex Federspiel, Eunji Kwon, Anusha Rahman
- Background When learning about functions, we have covered a bunch of different types of functions. From quadratic to cubic functions, from even and odd functions to function tra…
By Anusha Rahman
- Piecewise Functions Next in our lessons of types of functions, we will learn about piecewise functions. A piecewise function is a function that has different rules (or formulas)…
By Anusha Rahman
Problems 22
- Evaluate f(−1),f(0),f(2),f(4)f(-1), f(0), f(2), f(4)f(−1),f(0),f(2),f(4) in order, where f(x)={x2−2ifx<24+∣x−5∣ifx≥2.f(x)=\left\{\begin{matrix} x^2-2&if&x<2\\ 4+|x-5|&if&x\geq2.…
- Evaluate f(−1),f(0),f(2),f(4)f(-1), f(0), f(2), f(4)f(−1),f(0),f(2),f(4), where f(x)={4−x3ifx<1x+1ifx≥1.f(x)=\left\{\begin{matrix} 4-x^3&if&x<1\\ \sqrt{x+1}&if&x\geq1. \end{matr…
- Evaluate f(−1),f(0),f(2),f(4)f(-1), f(0), f(2), f(4)f(−1),f(0),f(2),f(4) in order, where f(x)={5xifx<03if0≤x≤3x2ifx>3.f(x)=\left\{\begin{matrix} 5x&if&x<0\\ 3&if&0\leq x\leq3\\ …
- Define f(x)f(x)f(x) as follows: For every integer kkk, if x∈[k,x+1)x \in [k, x+1)x∈[k,x+1), let f(x)=k(x+1)−k2f(x) = k(x+1) - k^2f(x)=k(x+1)−k2. What is f(123456789)f(123456789)…
- Evaluate f(1),f(2),f(5) and f(16)f(1), f(2), f(5) \text{ and } f(16)f(1),f(2),f(5) and f(16) in order where f(x)={x3−1x2+1ifx<22x3+xif2≤x≤5x2+1ifx>5f(x)= \left\{\begin{matrix} x…
- Evaluate f(−1),f(0),f(3) and f(6)f(-1), f(0), f(3) \text{ and } f(6)f(−1),f(0),f(3) and f(6) in order where f(x)={xx3−1ifx<−0.5x2+2x+1if−0.5≤x≤3x3ifx>3f(x)= \left\{\begin{matrix…
- Evaluate f(−1),f(0),f(1) and f(5)f(-1), f(0), f(1) \text{ and } f(5)f(−1),f(0),f(1) and f(5) in order where f(x)={x+1x2ifx≤−15+1x2+1if−1<x≤15ifx>1f(x)= \left\{\begin{matrix} \df…
- Evaluate f(−1),f(0),f(2)f(-1), f(0), f(2)f(−1),f(0),f(2), and f(4)f(4)f(4) in order where f(x) = \left{\begin{matrix} 3 &\text{if}& x\leq -1 \ -x^{4}-1 &\text{if}& -1< x\leq \df…
- Evaluate f(−3)f(-3)f(−3), f(0)f(0)f(0), and f(1)f(1)f(1) in order where f(x) = \left{\begin{matrix} 5x+1 &\text{if}& x \leq 0 \ x^{3} &\text{if}& x > 0 \ \end{matrix}\right.
- Evaluate f(−50),f(0)f(-50), f(0)f(−50),f(0), and f(3)f(3)f(3) in order where f(x)= \left{\begin{matrix} \sqrt {-x-1} + 3 &\text{if}& x<-1 \ x - 1 &\text{if}& -1 \le x \leq 2 \ x…
- Evaluate the function for f(2)f(2)f(2). f(x)={3ifx≤02ifx>0f(x)= \left\{\begin{matrix} 3 &\text{if}& x \le 0 \\ 2 &\text{if}& x> 0 \\ \end{matrix}\right.f(x)={32ififx≤0x>0
- Evaluate the function for f(−4)f(-4)f(−4) f(x)= \left{\begin{matrix} \dfrac{1}{2}x-4 &\text{if}&x \leq -2 \ 3-2x &\text{if}& x > -2 \ \end{matrix}\right.
- Evaluate the function for f(9)f(9)f(9). f(x)= \left{\begin{matrix} 2 -x &\text{if}& x \leq5 \ x^{2} &\text{if}& 5 < x < 8 \ 6 &\text{if}& x \geq 8 \ \end{matrix}\right.
- Evaluate the function g(−5)g(-5)g(−5). g(x)={15ifx≤−5xif−5<x<17−x4ifx>1g(x)= \left\{\begin{matrix} 15 &\text{if}& x \leq -5 \\ x &\text{if}& -5 < x < 1 \\ 7 - \dfrac {x}{4} &\te…
- Evaluate the function for f(1)f(1)f(1). f(x)= \left{\begin{matrix} x + 1 &\text{if}& x < 0 \ -x +1 &\text{if}& 0 \leq x \leq 2 \ x - 1 &\text{if}& x > 2 \ \end{matrix}\right.
- Evaluate the function for f(0)f(0)f(0). f(x)={x27if−5<x<−1(x−3)(x2−4)if−1≤x<299ifx≥2f(x)= \left\{\begin{matrix} \dfrac{x^{2}}{7} &\text{if}& -5 < x < -1 \\ (x-3)(x^{2}-4) &\text…
- Evaluate the function for f(3)f(3)f(3). f(x)= \left{\begin{matrix} x-1 &\text{if}& x \le -2 \ x^{3} + 4 &\text{if}& -2 < x < 3 \ \sin (x) &\text{if}& x > 3 \ \end{matrix}\right.
- Shelby is planning to pick up carpet squares for her new room. At Home Depot, the cost CCC (in dollars) of purchasing carpet squares, depending on the square feet xxx of the car…
- Evaluate f(1),f(5), and f(12)f(1), f(5), \text{ and } f(12)f(1),f(5), and f(12), where f(x)={x3+7x+5 if x≤5x2+4x if 5<x<20f(x)=\left\{\begin{matrix} x^3+7x+5 &\text{ if }& x \le…
- Evaluate f(5)f(5)f(5) where f(x)={35x+∣5x2−8∣ if x≤6∣14x2∣ if 6<xf(x)=\left\{\begin{matrix} \dfrac{3}{5}x+|5x^2-8| &\text{ if }& x \le 6 \\ |\dfrac{1}{4}x^2| &\text{ if }& 6 < x…
- Evaluate f(−3),f(0),f(3),f(5),f(-3), f(0), f(3), f(5),f(−3),f(0),f(3),f(5), where f(x)={x2+5x if x≤−2x+∣x−9∣ if −2<x<5x−3 if x≥5f(x)=\left\{\begin{matrix} x^2+5x &\text{ if }& x…
- Evaluate f(−4),f(3),f(7)f(-4), f(3), f(7)f(−4),f(3),f(7) where f(x)={x3+5x−6 if x≤413x+2 if x≥5f(x)=\left\{\begin{matrix} \dfrac {x^3+5}{x-6} &\text{ if }& x \le 4 \\ \dfrac{13}…