1. What are absolute value functions?
Absolute value functions are mathematical expressions that determine the distance of a number from zero on a number line, regardless of its sign. It is denoted by |x|.
2. What does the graph of an absolute value function look like?
The graph of an absolute value function is V-shaped with its vertex at the origin or some other point on the coordinate plane.
3. How do you graph the absolute value function y = |x|?
– Plot the points (x, |x|) for various values of x.
– Connect the points with straight lines to form the V-shaped graph.
4. How do you graph the absolute value function y = |x – a|?
– Shift the graph of y = |x| a units to the right if a is positive, or a units to the left if a is negative.
5. How do you graph the absolute value function y = a|x|?
– Multiply the y-values of y = |x| by a to stretch or compress the graph vertically.
6. How do you graph the absolute value function y = a|x – b| + c?
– Shift the graph of y = a|x| c units up if c is positive, or c units down if c is negative.
7. How do you find the vertex of an absolute value function?
The vertex of an absolute value function y = |x – h| + k is at the point (h, k).
8. How do you identify the slope of an absolute value function?
The slope of an absolute value function is undefined, as the graph does not have a constant rate of change.
9. How do you determine if a point is on the graph of an absolute value function?
Substitute the x-coordinate of the point into the equation of the absolute value function to find the corresponding y-coordinate. If the y-coordinate matches the actual y-coordinate of the point, then it lies on the graph.
10. How do you graph the absolute value function y = |ax + b|?
– Transform the graph of y = |x| by stretching or compressing it horizontally by a and shifting it b units to the left if b is positive or b units to the right if b is negative.
11. How do you find the x-intercepts of an absolute value function?
To find the x-intercepts of an absolute value function, set y = 0 and solve for x to determine the points where the graph intersects the x-axis.
12. How do you graph the absolute value function y = a|x + b| – c?
– Shift the graph of y = a|x| c units down if c is positive, or c units up if c is negative.
Drawing absolute value functions can be a straightforward process once you understand the basic principles involved. By following the steps outlined above and practicing with different absolute value functions, you can enhance your graphing skills and gain a deeper understanding of mathematical concepts.