Absolute Value Functions and Graphs, in Depth
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- Absolute Value Think of the absolute value of a real number the distance from 000 it is on the number line. |484848| is 484848, because 484848 is that distance away from 000. No…
By Vivian Loh, Alex Federspiel, Anusha Rahman
- (Video) Graphing Absolute Functions by mathman1024 Here's a video by mathman1024 showing you how to graph absolute value functions. Summary In this video, you will learn how to …
By Alex Federspiel, Anusha Rahman
- Absolute Value Functions & Graphs An absolute value function is a type of function where the output is always positive or zero, no matter what number you put in. The absolute va…
By Anusha Rahman
Problems 20
- Find the enclosed area of the following: ∣x∣+∣y∣=1|x| + |y| = 1∣x∣+∣y∣=1.
- True or False\text{True or False}True or False === The function f(x)=∣−2x∣+3f(x)=|-2x|+3f(x)=∣−2x∣+3 is graphed above.
- True or False\text{True or False}True or False === The function f(x)=∣2x+5∣+4f(x)=|2x+5|+4f(x)=∣2x+5∣+4 is graphed above.
- True or False\text{True or False}True or False === The function f(x)=3∣x−1∣f(x)=3|x-1|f(x)=3∣x−1∣ is graphed above.
- True or False\text{True or False}True or False === The function f(x)=−4∣4x+3∣−2f(x)=-4|4x+3|-2f(x)=−4∣4x+3∣−2 is graphed above.
- True or False\text{True or False}True or False === The function f(x)=−∣−x−5∣−1f(x)=-|-x-5|-1f(x)=−∣−x−5∣−1 is graphed above.
- Write the equation of the graph shown.
- The absolute value graph of what form can represent translations, reflections, stretches, or compressions of the "base graph" y=∣x∣y = |x|y=∣x∣?
- In the general form for the absolute value function, y=a∣x−h∣+k,y=a|x-h|+k,y=a∣x−h∣+k, what represents the vertex?
- In the equation for the general form of the absolute value function, y=a∣x−h∣+ky=a|x-h|+ky=a∣x−h∣+k, what does aaa represent?
- What shows the graph of the absolute value function y=∣x∣y=|x|y=∣x∣ being transformed to y=4∣x+1∣+2y=4|x+1|+2y=4∣x+1∣+2?
- Write the function that is graphed above.
- Which of the following is a graph of f(x)=∣x+4∣−2f(x)=|x+4|-2f(x)=∣x+4∣−2
- What is the vertex of the function f(x)=−2(∣x−3∣+2)f(x)=-2(|x-3|+2)f(x)=−2(∣x−3∣+2)?
- Write the transformation of f(x)=∣x∣f(x)=|x|f(x)=∣x∣ that is shifted left 171717 units, opens downward, and is vertically stretched two times as much as the original function.
- Liz is looking at the side of a pyramid. It is an equilateral triangle with the top of the triangle at the point (0,6)(0,6)(0,6) and meets the ground at the points (−4,0)(-4,0)(…
- What is the function of the graph above?
- What is the most basic form of the absolute value function? Which graphed function above is that function?
- Which of the functions in the graph above show a translation from f(x)=∣x+2∣−1f(x)=|x+2|-1f(x)=∣x+2∣−1 to g(x)=∣x−2∣+1g(x)=|x-2|+1g(x)=∣x−2∣+1?
- Which of the functions in the graph above show a transformation from f(x)=∣x+4∣−2f(x)=|x+4|-2f(x)=∣x+4∣−2 to g(x)=−2∣x−12∣+2g(x)=-2|x-\frac{1}{2}|+2g(x)=−2∣x−21∣+2?