Given: f(x) = 8 - 4x
A. Find f(-2)
B. Find x, when f(x) = 8
C. Graph the function.
D. State the domain and range of the function.
E. Use the graph to find x, when f(x) = 0. Show details on the graph.
F. Use the graph to find f(x) when x = 3. Show details on the graph.
f(x) = 8-4x
A f(2) = 8-4(-2)
B 8-4x = 8
C Now you have two points. Draw the line connecting them
D all real numbers. Think about it. Pick any x you want, and y is defined. A line goes out forever in both directions.
E,F now use the graph.
If it's you who has posted this several time now, please stop reposting it unless you get stuck on some part of the offered solutions...
are the points x or y?
To answer these questions, let's break them down step by step.
A. To find f(-2), we need to substitute x with -2 in the given function f(x) = 8 - 4x.
So, f(-2) = 8 - 4(-2).
Simplifying further, f(-2) = 8 + 8 = 16.
B. To find x when f(x) = 8, we substitute f(x) with 8 in the function.
8 = 8 - 4x
Adding 4x to both sides, we get 4x = 0.
Dividing both sides by 4, we find x = 0.
C. To graph the function, we can plot a few points and draw a line connecting them.
Let's choose a few x-values and find their corresponding y-values using the function.
For example, if we take x = -2, we know from A that f(-2) = 16.
Similarly, if we take x = 0, we know from B that f(0) = 8.
For x = 2, we find f(2) = 8 - 4(2) = 0.
Now we have three points: (-2, 16), (0, 8), and (2, 0).
Plotting these points on a graph, we can draw a straight line passing through them.
D. The domain of a function refers to all possible x-values. In this case, there are no restrictions on x, so the domain is (-∞, ∞), meaning the function is defined for all x.
The range of a function refers to all possible y-values. Looking at the graph, we can see that the function covers all real numbers because the line extends indefinitely in both upward and downward directions, so the range is also (-∞, ∞).
E. To find x when f(x) = 0 using the graph, we need to locate the y-value 0. Looking at the graph, we can see that the function intersects the x-axis at x = 2. Therefore, x = 2 is the solution when f(x) = 0.
F. To find f(x) when x = 3 using the graph, we need to locate the x-value 3. Looking at the graph, we can find the corresponding y-value on the line. From the point (2, 0), we can see that as we move one unit to the right (increasing x by 1), we move two units down (decreasing y by 2). Therefore, when x = 3, we can estimate f(x) to be -2 according to the graph.
I hope this explanation helps you understand the steps to find the answers!