Use the graphs of f and g to solve Exercises 83–90. Find (g-f) (-2).
Verified step by step guidance
1
Step 1: Understand the problem. You are tasked with finding the value of (g - f)(-2), which means you need to subtract the value of f(-2) from g(-2).
Step 2: Locate the x-coordinate of -2 on the graph. Look at the vertical line corresponding to x = -2 and identify the points where the functions f(x) (blue curve) and g(x) (red curve) intersect this line.
Step 3: Determine the value of f(-2). Find the y-coordinate of the blue curve at x = -2. This is the value of f(-2).
Step 4: Determine the value of g(-2). Find the y-coordinate of the red curve at x = -2. This is the value of g(-2).
Step 5: Subtract f(-2) from g(-2). Use the formula (g - f)(-2) = g(-2) - f(-2) to compute the result.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1m
Play a video:
0 Comments
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Evaluation
Function evaluation involves substituting a specific input value into a function to determine its output. In this case, we need to evaluate both functions f and g at x = -2 to find their respective values. This is a fundamental skill in algebra, as it allows us to analyze the behavior of functions at specific points.
The difference of two functions, denoted as (g - f)(x), is calculated by subtracting the output of function f from the output of function g for the same input x. This operation helps in understanding how the two functions compare at any given point, which is essential for solving the problem at hand.
Interpreting graphs involves analyzing the visual representation of functions to extract information about their values, trends, and intersections. In this exercise, we will use the graph to find the values of f(-2) and g(-2) directly from the plotted points, which is crucial for accurately calculating (g - f)(-2).