Function notation is used to write the equation of a function. Function notation simply sets an expression equal to f(x), read "f of x," which means "f is a function of x."
You may use any letter to represent a function: f(x), g(x), h(x), r(x), etc.
When given an equation in function notation (for example: f(x) = x + 1), you may be asked to do one of the following:
•Evaluate the function for a given x-value—substitute the value for x and simplify.
•Solve for x given a function value—substitute the function value and solve for x.
When given a table or a graph, you may be asked to do one of the following:
•Given an output value, identify the input value that corresponds.
•Given an input value, identify the output value that corresponds.
With any function, you can write inputs and outputs as ordered pairs: (input, output).
•Slope is the "rise over run."
•Slope is the ratio of the vertical change to the horizontal change between two points.
•Given the line graphed on a coordinate plane, you find any two points on the line and count the rise (up or down) and the run (side to side) between the two points. Start with the point on the left. If you have to go up, your rise is positive. If you have to go down, your rise is negative. Since you always go to the right, your run will always be positive.
•To graph a line using its x- and y- intercepts: •Find the x-intercept: replace y with the number zero and solve for x.
•Find the y-intercept: replace x with the number zero and solve for y.
•Plot both intercepts on the coordinate plane, and then connect them to draw the graph.
Remember that the x-intercept can be written as an ordered pair where y is zero. The y-intercept can be written as an ordered pair where x is zero.
(2, 0) x-intercept
(0, −3) y-intercept
•To graph a line using the slope-intercept form: •Manipulate the equation into slope-intercept form, y = mx + b.
•Identify and plot the y-intercept of the line. Remember, the y-intercept is b. Don't forget: The sign goes with the number.
•Identify and use the slope of the line to find a second point. Remember, the slope is m. Don't forget: Starting at the y-intercept, the numerator tells you the rise (count up if positive and down if negative), the denominator tells you the run (count right.)
•Draw a straight line through the two points to complete the graph.