Given a function, we can graph the x and y values to obtain a pictorial representation of their relationship. The following steps outline the ways to graph a function.
Step 1: Find the x and y intercepts. x-intercept is the point where the graph meets the x-axis. At this point, y will be equal to 0. Similarly y-intercept is the point where the graph meets the y-axis. At this point, x will be equal to 0.
For x-intercept, y = 0
For y-intercept, x = 0
For the function y = f(x) = x2 + 5x + 6, we can find the x and y intercepts by using y = 0 to get the x intercept, and x = 0 to get the y intercept.
When y = 0, x2 + 5x + 6 will be equal to 0. We need to solve the equation to get the x intercept/s. So
x2 + 5x + 6 = 0
(x + 3) (x + 2) = 0
x = -3 or -2.
x-intercepts therefore are (-3, 0) and (-2, 0).
When x = 0, y = f(x) = x2 + 5x + 6 will be
y = 02 + 5×0 + 6
= 0 + 0 + 6
y-intercept is (0, 6).
Step 2: Find if the function is odd or even. This will help you to draw the graph of the function quicker.
y = f(x) = x2 + 5x + 6
f(-x) = (-x)2 + 5 (-x) + 6
= x2 – 5x + 6
This function is neither even nor odd.
Step 3: Find where does the curve of a function increase or decrease in a domain.
The function decreases when x < -2.5 (concave down), and increases when x > -2.5 (concave up)
Step 4: Find the stationary point of the function/curve, and check if it is the maximum or the minimum point for the function/curve.
The stationary point is (-2.5, -0.25).
Here the minimum value is -0.25.
Here are more lessons on graphing functions that are: