Think of the expressions on both sides of the equals sign as two functions.
x≈ 3.2
Practice makes perfect
To solve the given equation by graphing, let's think of the expressions on both sides of the equals sign as being about two functions. Let's call them f(x) and g(x).
f(x)=5-x g(x)=sqrt(x)
Notice that f(x) is a straight line and g(x) is a radical function. The straight line we can graph by using its y-intercept and slope to find a pair of points through which the line passes.
To draw the radical function we need to find some ordered pairs through which its graph passes. Note that the radicand of a square root is always non-negative. Therefore, the lowest possible value of x must be x=0.
With this information, we can calculate some ordered pairs for g(x).
x
sqrt(x)
g(x)
0
sqrt(0)
0
1
sqrt(1)
1
4
sqrt(4)
2
9
sqrt(9)
3
Using this information, we can graph the second function as well.
To estimate the point of intersection, we will zoom in around where the graphs cross each other.
The solution to the equation is the x-value of the point where the graphs intersect. As we can see, the graphs intersect at around (3.2,1.8). Therefore, the solution to the equation must be x≈ 3.2.
