How do you find the axis of symmetry for an absolute value function?

Linear “pieces” will appear in the equation of the absolute value function in the following manner: y = | mx + b | + c where the vertex is (-b/m, c) and the axis of symmetry is x = -b/m. Note that the slope of the linear “pieces” are +1 on the right side and -1 on the left side.

How do you know if a function has no symmetry?

A curve cannot be a function when a vertical line interesects it more than once. And a curve that is symmetrical around the x-axis will always fail the vertical line test (unless that function is f(x) = 0). So, a function can never be symmetrical around the x-axis.

Are absolute value functions symmetric?

An absolute value graph is symmetrical, meaning it can be folded in half on its line of symmetry.

How do you know if a function is symmetric?

Algebraically check for symmetry with respect to the x-axis, y axis, and the origin. For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.

How do you find the absolute value of a function?

More generally, the form of the equation for an absolute value function is y=a| x−h |+k.

Is the absolute value function even?

It is an even function.

Does the absolute value function intersect the horizontal axis?

Figure 7 (a) The absolute value function does not intersect the horizontal axis. (b) The absolute value function intersects the horizontal axis at one point. (c) The absolute value function intersects the horizontal axis at two points. In Other Type of Equations, we touched on the concepts of absolute value equations.

Is the expression inside the absolute value symbol a single variable?

This problem is getting interesting since the expression inside the absolute value symbol is no longer just a single variable. Don’t worry; the set-up remains the same. Just be careful when you break up the given absolute value equation into two simpler linear equations, then proceed how you usually solve equations.

What is the equation for an absolute value function?

More generally, the form of the equation for an absolute value function is y = a | x − h | + k. Also: The vertex of the graph is ( h, k). The domain of the graph is set of all real numbers and the range is y ≥ k when a > 0.

How do you find the domain and axis of symmetry?

The vertex of the graph is ( h, k). The domain of the graph is set of all real numbers and the range is y ≥ k when a > 0. The domain of the graph is set of all real numbers and the range is y ≤ k when a < 0. The axis of symmetry is x = h. It opens up if a > 0 and opens down if a < 0.