Step Functions
Read this topicExplanations 4
- (Video) Heaviside Function by PatrickJMT This video by patrickJMT explores the Heaviside function, defined via: H(x)={0x<01x≥0H(x)=\begin{cases} 0 & x<0 \\ 1 & x\geq 0 \\ \end{c…
By Alex Federspiel, Liza Sulkin, Victor Wang, Anusha Rahman
- What is a step function? A step function is a piecewise function over the real numbers that is made up from a finite number of constant functions. The name comes from the resemb…
By Liza Sulkin
- Examples of step functions\text{Examples of step functions}Examples of step functions Floor and ceiling functions The floor function, f(x)=⌊x⌋f(x)=\lfloor x \rfloorf(x)=⌊x⌋ (als…
By Liza Sulkin, Anusha Rahman
- Step Functions Our next type of piecewise function is the step function! A step function looks exactly like it sounds: a series of steps! The following is an example of a step f…
By Anusha Rahman
Problems 20
- Define a piecewise step function as follows: For every k∈Zk \in \mathbb{Z}k∈Z (integers), if x∈[2k,2k+1)x \in [2^k, 2^{k+1})x∈[2k,2k+1) then f(x)=kf(x) = kf(x)=k. If x≤0x \le 0x…
- Where does the jump discontinuity occur for H(2n−1)H(2n-1)H(2n−1)?
- Does H(−n)H(-n)H(−n) flip the function vertically or horizontally?
- For the function n3[H(n−1)−H(n−3)]n^3[H(n-1)-H(n-3)]n3[H(n−1)−H(n−3)] what is the value at n=3n=3n=3?
- For the function n3[H(n−1)−H(n−3)]n^3[H(n-1)-H(n-3)]n3[H(n−1)−H(n−3)] what is the value at n=2n=2n=2?
- Suppose we have a function h(n)=g(n)[H(n−1)−H(n−3)]h(n) = g(n)[H(n-1)-H(n-3)]h(n)=g(n)[H(n−1)−H(n−3)]. Select the function that g(n)g(n)g(n) could be in order for h(n)h(n)h(n) t…
- Suppose we have a function h(n)=g(n)[H(n−1)−H(n−3)]h(n) = g(n)[H(n-1)-H(n-3)]h(n)=g(n)[H(n−1)−H(n−3)]. Select the function that g(n)g(n)g(n) could be in order for h(n)h(n)h(n) t…
- Let f(x)=[x]f(x)=[x]f(x)=[x], where [x][x][x] denotes the greatest integer less than or equal to xxx. Find f(−2.009)f(-2.009)f(−2.009).
- Which of the following represents rounding xxx to the nearest integer? (You may round 0.5 either up or down.)
- If you drive around for x≥1x\geq1x≥1 hours before returning the car, how much money does the rental company charge?
- You only have 12\1212 to spend on a phone call. What is the longest possible call you could make?
- If there are 888 people in line at each post office, which one will have the shortest wait time?
- Why is the graph above not a step function?
- What could the following expression equal? ⌈x⌉−⌊x⌋\lceil x \rceil - \lfloor x \rfloor⌈x⌉−⌊x⌋
- What could the following expression equal? ⌊x⌋−⌈x⌉\lfloor x \rfloor-\lceil x \rceil⌊x⌋−⌈x⌉
- If ⌈x⌉=n\lceil x \rceil=n⌈x⌉=n, which of the following is true? Give the most specific correct answer.
- If ⌊x⌋=n\lfloor x \rfloor=n⌊x⌋=n, which of the following is true? Give the most specific correct answer.
- If ⌊x⌋=n\lfloor x \rfloor=n⌊x⌋=n, which of the following is true? Give the most specific correct answer.
- If ⌈x⌉=n\lceil x \rceil=n⌈x⌉=n, which of the following is true? Give the most specific correct answer.
- Is a constant function a step function?