Y=4x³-2
This is a cubic function, where the variable Y depends on the variable x. The equation states that Y equals 4 times x cubed, minus 2.
To graph this function, we can choose different values of x and find the corresponding values of Y. For example, if we choose x=0, then Y=-2. If we choose x=1, then Y=2. If we choose x=-1, then Y=-6.
We can then plot these points on a coordinate plane and connect them to get a graph of the function. Since it is a cubic function, the graph will have a general shape of a "s" curve that passes through the point (0,-2) and has steep rises and falls.
To graph the equation y = 4x^3 - 2, follow these steps:
Step 1: Plot the x and y-axis on a graph paper.
Step 2: Choose some values for x and calculate the corresponding y-values using the equation.
Let's take x = -2, -1, 0, 1, and 2.
When x = -2 -> Substitute x = -2 into the equation: y = 4(-2)^3 - 2 = 4(-8) - 2 = -32 - 2 = -34
So when x = -2, y = -34
When x = -1 -> Substitute x = -1 into the equation: y = 4(-1)^3 - 2 = 4(-1) - 2 = -4 - 2 = -6
So when x = -1, y = -6
When x = 0 -> Substitute x = 0 into the equation: y = 4(0)^3 - 2 = 4(0) - 2 = 0 - 2 = -2
So when x = 0, y = -2
When x = 1 -> Substitute x = 1 into the equation: y = 4(1)^3 - 2 = 4(1) - 2 = 4 - 2 = 2
So when x = 1, y = 2
When x = 2 -> Substitute x = 2 into the equation: y = 4(2)^3 - 2 = 4(8) - 2 = 32 - 2 = 30
So when x = 2, y = 30
Step 3: Plot the points (-2, -34), (-1, -6), (0, -2), (1, 2), and (2, 30) on the graph.
Step 4: Connect the points with a smooth curve. Since the equation is a cubic function, the curve should have a s-shaped form.
Step 5: Label the axes as x and y, and provide a title for the graph.
That's it! You have now graphed the equation y = 4x^3 - 2.