Question

use the picture of the graphs of g(x) and f(x) to answer the questions. remember if the graph hits the edge of the window it means that it continues on. what is the domain of g(x)? use interval notation. what is the range of g(x)? use interval notation. what is the domain of f(x)? use interval notation. g(4)= g(x)=1 has f(5)= f(x)=3 when the slope of the y - intercept therefore, the equation of f(x) is for what values of x does f(x)=g(x)? x = and x = when is f(x)≥g(x)? f(10)=

Explanation:

Step1: Determine domain of g(x)

The graph of g(x) extends infinitely in both x - directions. So the domain is all real numbers, represented as $(-\infty,\infty)$.

Step2: Determine range of g(x)

The graph of g(x) extends infinitely down - ward and has a maximum value of 4 (open - circle at (0,4)). So the range is $(-\infty,4)$.

Step3: Determine domain of f(x)

The graph of f(x) extends infinitely in both x - directions. So the domain is $(-\infty,\infty)$.

Step4: Find g(4)

Locate x = 4 on the x - axis, then find the corresponding y - value on g(x). g(4)=0.

Step5: Find x for g(x)=1

Locate y = 1 on the y - axis, then find the x - values where g(x) intersects y = 1. There are two intersection points, so g(x)=1 has two solutions.

Step6: Find f(5)

Locate x = 5 on the x - axis, then find the corresponding y - value on f(x). f(5)=3.

Step7: Find x for f(x)=3

Locate y = 3 on the y - axis, then find the x - values where f(x) intersects y = 3. There is one intersection point, so f(x)=3 has one solution.

Step8: Find equation of f(x)

The line f(x) has a y - intercept of - 2 and a slope of 1. Using the slope - intercept form y=mx + b, the equation of f(x) is y=x - 2.

Step9: Find x for f(x)=g(x)

Find the intersection points of f(x) and g(x). They intersect at x = 2 and x = 6.

Step10: Find when f(x)≥g(x)

Observe the graph to see where the graph of f(x) is above or on the graph of g(x). This occurs when $2\leq x\leq6$.

Step11: Find f(10)

Substitute x = 10 into f(x)=x - 2. f(10)=10 - 2=8.

Answer:

Domain of g(x): $(-\infty,\infty)$
Range of g(x): $(-\infty,4)$
Domain of f(x): $(-\infty,\infty)$
g(4): 0
g(x)=1 has: two solutions
f(5): 3
f(x)=3 has: one solution
Equation of f(x): y=x - 2
x for f(x)=g(x): 2 and 6
When f(x)≥g(x): $2\leq x\leq6$
f(10): 8