How do you write an equation reflected over the x-axis?

The rule for a reflection over the x -axis is (x,y)→(x,−y) .

How do you determine a function from an equation?

If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function. Using the vertical line test, all lines except for vertical lines are functions.

How do you determine if a function is even or odd?

You may be asked to “determine algebraically” whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even.

How do you find the transformation of an equation?

The function translation / transformation rules:

1. f (x) + b shifts the function b units upward.
2. f (x) – b shifts the function b units downward.
3. f (x + b) shifts the function b units to the left.
4. f (x – b) shifts the function b units to the right.
5. –f (x) reflects the function in the x-axis (that is, upside-down).

What does reflected over the x axis mean?

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

How do you find the equation of a line that is reflected?

The equation for your reflected line can be constructed using the point-slope form, y=m(x−xQ)+yQ. The point (xQ,yQ) is easily obtained as the intersection of your “mirror” line (the blue one) and the line to be reflected (the solid red one).

What makes something an odd function?

A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f. An interactive LiveMath notebook to visualize symmetry with respect to the y-axis. An interactive LiveMath notebook to determine when a function is odd.

What does it mean for a function to be even odd or neither?

If we get an expression that is equivalent to f(x), we have an even function; if we get an expression that is equivalent to -f(x), we have an odd function; and if neither happens, it is neither!

What is transformation form?

The transformational form of an equation is a form that has. the x2 by itself. y = -x2. y = -x2 – 1. y = x2 + 8.