c When we equate two functions, we are calculating the x-value where they cross each other.
A
aGraph:
B
b (- 2.4,0.78)
C
c x≈ 2.4
Practice makes perfect
a 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=- 3.
x+3=0 ⇔ x= - 3
With this information, we can calculate some ordered pairs for g(x).
x
sqrt(x+3)
g(x)
-3
sqrt(-3+3)
0
-2
sqrt(-2+3)
1
-1
sqrt(-1+3)
1.41
0
sqrt(0+3)
1.73
1
sqrt(1+3)
2
2
sqrt(2+3)
2.24
3
sqrt(3+3)
2.45
Using this information, we can graph the second function as well.
b To estimate the point of intersection, we will zoom in around where the graphs from Part A cross each other.
As we can see, the graphs intersect at around (- 2.4,0.78).
c The solution to the equation is the x-value where the graphs intersect. From Part B, we estimated the point of intersection to (- 2.4,0.78). Therefore, the solution to the equation must be x≈ - 2.4.
