Read: Graph Radical Functions
Learning Objectives
- Graph a radical function using a table of values
- Identify how multiplication can change the graph of a radical function
- Identify how addition and subtraction can change the graph of a radical function
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Example
Match each of the following functions to the graph that it represents. a) b) c) a)![A black curving line going up and right labeled g(x) equals the square root of x. A curved red line going right and further up than the black line.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/04/18232459/image027.gif)
![A black curving line going up and right labeled g(x) equals the square root of x. A curved red line that is a mirror of the black line over the x axis so that the red line is going to the right and down.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/04/18232500/image028.gif)
![A black curving line going up and right labeled g(x) equals the square root of x. A red line that goes to the right and not as far up as the black line.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/04/18232501/image029.gif)
Answer:
Function a) means that all the outputs will be negative - the function is the negative of the square roots of the input. This will give the other half of the parabola on it's side. Therefore the graph
goes with the function
Function b) means take the square root of all the inputs, then multiply by two, so the outputs will be larger than the outputs for . The graph
goes with the function
Function c) means take the squat=re root of the inputs then multiply by . The outputs will be smaller than the outputs for . The graph
goes with the function .
Answer
Function a) goes with graph b) Function b) goes with graph a) Function c) goes with graph c)Example
Match each of the following functions to the graph that it represents. a) b) a)![A black curving line going up and right labeled g(x) equals the square root of x. A curved red line much like the black line but starting at 0, negative 2.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/04/18232502/image030.gif)
![DM_U17_Final1stEd-11-12-12](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/07/01215107/DM_U17_Final1stEd-11-12-12-270x300.jpg)
Answer:
Function a) means take the square root of all the inputs and add three, so the out puts will be greater than those for , therefore the graph that goes with this function is
Function b) means take the square root of the input then subtract two. The outputs will be less than those for , therefore the graph that goes with this function is
Answer
Function a) goes with graph b) Function b) goes with graph a)Example
Match each of the following functions to the graph that it represents. a) b) a)![A black curving line going up and right labeled g(x) equals the square root of x. A curved red line much like the black line starting from 2,0](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/04/18232504/image032.gif)
![A black curving line going up and right labeled g(x) equals the square root of x. A curved red line much like the black line starting from negative 1, 0](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/04/18232503/image031.gif)
Answer:
Function a) adds one to the inputs before the square root is taken. The outputs will be greater, so it ends up looking like a shift to the left. The graph that matches this function is
Function b) means subtract before the square root is taken. This makes the outputs less than they would be for the standard , and looks like a shift to the right. the graph that matches this function is
Answer
Function a) matches graph b) Function b) matches graph a)Example
Graph .Answer: Before making a table of values, look at the function equation to get a general idea what the graph should look like. Inside the square root, you’re subtracting , so the graph will move to the right from the basic graph. You’re also adding outside the square root, so the graph will move down two from the basic graph. Create a table of values. Choose values that will make your calculations easy. You want to be a perfect square (, and so on) so you can take the square root.
x | f(x) |
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![A black curving line going up and right labeled g(x) equals the square root of x. A curved red line much like the black line starting from negative 1, 0](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/04/18232503/image031.gif)
Answer
![A black curving line going up and right labeled g(x) equals the square root of x. A curved red line much like the black line starting from 2,0](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/04/18232504/image032.gif)