Introduction to Graph a Function
Graph a function refers to the set of all the ordered pairs, such that ‘x’ comes in the domain of the function ‘f’. A graph of a function refers to a visual representation of a function’s behaviour on an x-y plane. Furthermore, the graphs facilitate in gaining a proper understanding of the various aspects of a function.
An individual can graph a huge number of equations. Furthermore, there are different formulas available for these various equations. Most noteworthy, there will always be ways to graph a function in case an individual forgets the steps for a particular type of function.
Graph a Function by Plotting Points
Here, one must first of all find points of a function. In order to find these points, one can choose input values. Then one must evaluate the function at these input values and afterwards calculate these values. Moreover, the input values and output values form the coordinate pairs.
Then one must plot these coordinate pairs on a grid. Furthermore, the evaluation of the function must take place at a minimum of two points. This is so that the least two points on the graph of the function may be found.
An example can be the function f(x)=2x, for this one can use the input values 1 and 2. If one evaluates the function for an input value of 2, then it yields an output value of 4 whose representation is by the point (1, 2). So, evaluating the function for an input value of 2 yields an output value of 4 whose representation is by the point (2, 4).
Most noteworthy, choosing three points is almost always advisable. This is because, in case all the three fail to fall on the same line, then one can understand that an error was made.
y Intercept of a Function
Here one uses the specific characteristics of the function instead of plotting points. Moreover, the first characteristic happens to be the y-intercept.
This is certainly the point of zero input value. In order to find the y-intercept, set x = 0 in the particular equation.
The other characteristic of the function is certainly the slope. This refers to the measure of steepness.
One must recall that the slope happens to be the rate of change of the function. Moreover, the slope of the linear function is certainly equal to the ratio of the change in outputs to the change in inputs.
Another way to think about the slope is carrying out the division of the vertical difference, or rise, which is between any two points by the horizontal difference, or run. Above all, the slope of a linear function is always the same between any two points.
Graph a Function Using Transformations
Another option for graphing is to make use of transformations on the identity function f(x)=x. The transformation of a function may take place by a shift up, down, left, or right. Furthermore, the transformation of a function may also take place by using a reflection, stretch, or compression.
In the equation f(x)=mx, the m happens to be acting as the compression or the vertical stretch of the identity function. In case the m is negative, then there is also a vertical reflection of the graph.
One must notice that on multiplication of the equation (x) =x by m, the stretching of the graph of ‘f’ by a factor of m units results. Most noteworthy, this happens if m > 1 and compresses the graph of ‘f’ by a factor of m units in case 0 < m < 1. This means the larger the absolute value of m would consequently mean that the slope would be steeper.
Solved Question for You
Q1. Which of the following is not a way to graph a function
A. Graphing a function by plotting points
B. Graphing a function simplifying the x-intercept
C. Graphing a Function using y-intercept and slope
D. Graphing a function using transformations
A1. The correct option is B., which is “graphing a function simplifying the x-intercept.” This is because no such way to graph a function like this exists.