What Is a Function Transformation?
Read this topicExplanations 4
- (Video) Translating Absolute Value Functions by Keith Mann There are two ways we will learn to translate a function: Horizontal and Vertical. Keith Mann explains both. Skip to 3…
By Ben Ferrara, Alex Federspiel, Caroline K, Amy Feraco, Jonathan Heller, Anusha Rahman
- Function Transformation A function transformation is to move the graph by shifting the axis of the graph, stretch, or compress the graph. It take the basic function of f(x)f(x)f…
By Eunji Kwon, Anusha Rahman
- General Translations Here are the types of translations: Horizontally left Horizontally right Vertically down Vertically up The general form of the absolute value equation is y=…
By Amy Feraco
- Function Transformation A function transformation changes the way a function looks on a graph. There are three main types of transformations, which we will dive into deeper in f…
By Anusha Rahman
Problems 41
- Which is the graph of the equation y=∣x∣−4y=|x|-4y=∣x∣−4?
- Which is the graph of the equation y=∣x+4∣y=|x+4|y=∣x+4∣?
- Which is the graph of the equation y=∣x∣y=|x|y=∣x∣?
- If the scale on both axes is 111 (distance between neighboring tick marks is 111), which is the graph of the equation y=∣x−1∣+2y=|x-1|+2y=∣x−1∣+2?
- If the scale on both axes is 111 (distance between neighboring tick marks is 111), which is the graph of the equation y=∣x−3∣−1y=|x-3|-1y=∣x−3∣−1?
- If we start with the graph of y=∣x∣y = |x|y=∣x∣, and then translate 111 unit left and 222 units down, we get the graph of y=∣x+c∣+dy=|x+c|+dy=∣x+c∣+d. What are ccc and ddd equal…
- If we start with the graph of y=∣x∣y = |x|y=∣x∣, and then translate 222 units right and 111 unit up, we get the graph of y=∣x+c∣+dy=|x+c|+dy=∣x+c∣+d. What are ccc and ddd equal to?
- What is a vertex of an absolute value graph?
- Consider the graph of the function above. What is the formula for the graph of this absolute value function?
- Which of the following represents the transformation from the red function to the green function?
- Shifting an absolute value graph both vertically and horizontally shows a(n) _________ shift.
- 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?
- Which of the following represents the shift from y=3+∣x−2∣y=3+|x-2|y=3+∣x−2∣ to y=1−∣x+2∣y=1-|x+2|y=1−∣x+2∣?
- Consider the general form of the absolute value function y=∣x+c∣+dy=|x+c|+dy=∣x+c∣+d. In the graph above, how do variables ccc and ddd change when moved from the orange function…
- Arrange the equations showing movements in the absolute value graph in the following order: up kkk units, down kkk units, right hhh units, left hhh units
- In a translated absolute value function y=∣x−h∣+k,y=|x-h|+k,y=∣x−h∣+k, what represents the vertex?
- The absolute value graph of what form can represent translations of the "base graph" y=∣x∣y = |x|y=∣x∣?
- Which absolute value function below has a graph with vertex at (1,1)(1,1)(1,1)?
- Which absolute value function below has a graph with vertex at (−1,−1)(-1,-1)(−1,−1)?
- You have the graph of y=∣x∣y = |x|y=∣x∣ and decide to make another graph, for a function z,z,z, where you randomly do a horizontal translation of yyy of size −1,0,-1, 0,−1,0, or…
- What kind of transformation of f(x)f(x)f(x) would be y=af(x)y=af(x)y=af(x) when a>1a>1a>1?
- What kind of transformation of f(x)f(x)f(x) would be y=af(x)y=af(x)y=af(x) when 0<a<10<a<10<a<1?
- What kind of transformation of f(x)f(x)f(x) would be y=f(cx)y=f(cx)y=f(cx) when 0<c<10<c<10<c<1?
- What kind of transformation of f(x)f(x)f(x) would be y=f(cx)y=f(cx)y=f(cx) when c>1c>1c>1?
- What kind of transformation of f(x)f(x)f(x) would be y=−f(x)y=-f(x)y=−f(x)?
- What kind of transformation of f(x)f(x)f(x) would be y=f(−x)y=f(-x)y=f(−x)?
- What kind of transformation of f(x)f(x)f(x) would be y=f(x+c)y=f(x+c)y=f(x+c) when c>0c>0c>0?
- What kind of transformation of f(x)f(x)f(x) would be y=f(x+c)y=f(x+c)y=f(x+c) when c<0c<0c<0?
- What kind of transformation of f(x)f(x)f(x) would be y=f(x)+cy=f(x)+cy=f(x)+c when c<0c<0c<0?
- What kind of transformation of f(x)f(x)f(x) would be y=f(x)+cy=f(x)+cy=f(x)+c when c>0c>0c>0?
- Given g(x)g(x)g(x) is a downward shift of 12\frac{1}{2}21 from f(x)=x3f(x)=x^3f(x)=x3, what is the equation of g(x)g(x)g(x)?
- Given g(x)g(x)g(x) is an upward shift of 333 from f(x)=x2f(x)=x^2f(x)=x2, what is the function of g(x)g(x)g(x)?
- Given g(x)g(x)g(x) is a rightward shift of 222 from f(x)=xf(x)=\sqrt{x}f(x)=x, what is the function of g(x)g(x)g(x)?
- Given g(x)g(x)g(x) is a leftward shift of 222 from f(x)=1xf(x)=\frac{1}{x}f(x)=x1, what is the equation of g(x)g(x)g(x)?
- Given g(x)g(x)g(x) is a horizontal stretch of 222 from f(x)=x2f(x)=x^2f(x)=x2, what is the equation of g(x)g(x)g(x)?
- Given g(x)g(x)g(x) is a horizontal compression of 333 and a reflection over the yyy-axis from f(x)=x2f(x)=x^2f(x)=x2, what is the equation of g(x)g(x)g(x)?
- Given g(x)g(x)g(x) is a vertical compression of 222 and a reflection over the xxx-axis from f(x)=x4f(x)=x^4f(x)=x4, what is the equation of g(x)g(x)g(x)?
- Given g(x)g(x)g(x) is a vertical stretch of 444 and a reflection over the yyy-axis from f(x)=x2+2f(x)=x^2+2f(x)=x2+2, what is the function of g(x)g(x)g(x)?
- Given g(x)g(x)g(x) is f(x)f(x)f(x) shifted right 333 units and down 111 unit, and f(x)=x2f(x)=x^2f(x)=x2, what is the equation of g(x)g(x)g(x)?
- Given g(x)g(x)g(x) is f(x)f(x)f(x) shifted left 13\frac{1}{3}31 units and down 222 units, and f(x)=(x−1)2f(x)=(x-1)^2f(x)=(x−1)2, what is the equation of g(x)g(x)g(x)?