Algebra Relations and Functions: What You Need to Know

When, 

The graph obtained has two intercepts –the x-intercept and the y-intercept. The x-intercept refers to the value of x when the value of y is zero while the y-intercept refers to the value of y when that of x is zero. From the graph, the x-intercept is 5.33 (or 16/3), and the y-intercept is 4. The graph extends infinitely in both direction, and its domain of the equation is shown below. The range of the equation is also shown below. 

The equation is a function because, for each input, there is exactly one output. A function is defined in the OH Schools (N.d) as “a relationship in which each element of the domain is paired with exactly one element of the range.” A function shows how two variables are related. In mathematics, the vertical line test is used to visually determine if a curve is a graph of a function or not. If the curve cuts the XY –plane more than once then the curve has more than one value of y, and therefore, it does not represent a function. In this case, our graph cuts the XY –plane once and there it represents a function. 

When, 

The figure above shows the graph for equation . As seen on the graph, the equation has two intercepts –the x –intercept and the y –intercept, which are 0 and 0 respectively. The graph starts from 0 and extends infinitely in the right direction (positive). 

The equation is also a function because, for each input, there is exactly one output. 

Transformation 

A transformation is an operation happening to the primary function in some way. A function may be transformed by a shift up, down, left, or right. For instance, when we transform the equation and shift it by three units upward and four units to the left, the graph shifts and the equation changes completely. The intercepts also change. The new equation becomes; 

References 

OH Schools. (N.d). Functions. [Online]. Retrieved from: http://www.ohschools.k12.oh.us/userfiles/223/Classes/30/1-7%20Answers.pdf . Accessed 1 st August 2019.