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.
A. f(-2) = 8-4(-2)
B. 8-4x = 9
You have two points now. plot them and draw the line between them
A line goes forever in both directions, both horizontally and vertically, so ...
now look up the points for E and F
A. To find f(-2), we substitute -2 for x in the given function:
f(x) = 8 - 4x
f(-2) = 8 - 4(-2)
f(-2) = 8 + 8
f(-2) = 16
Therefore, f(-2) = 16.
B. To find x when f(x) = 8, we set the given function equal to 8 and solve for x:
f(x) = 8 - 4x
8 = 8 - 4x
0 = -4x
Dividing both sides of the equation by -4 gives us:
x = 0/(-4)
x = 0
Therefore, x = 0 when f(x) = 8.
C. To graph the function f(x) = 8 - 4x, we plot points on a coordinate plane. We choose different values for x and calculate the corresponding values of f(x). Let's choose three values to plot the graph.
When x = 0:
f(0) = 8 - 4(0)
f(0) = 8
When x = 1:
f(1) = 8 - 4(1)
f(1) = 8 - 4
f(1) = 4
When x = -1:
f(-1) = 8 - 4(-1)
f(-1) = 8 + 4
f(-1) = 12
Now we plot the points (0, 8), (1, 4), and (-1, 12) on the coordinate plane and connect them to form a straight line. This line represents the graph of the function f(x) = 8 - 4x.
D. The domain refers to the set of all possible input values of the function, and the range refers to the set of all possible output values.
For the given function f(x) = 8 - 4x, there are no restrictions on the input variable x, so the domain is all real numbers, or (-∞, +∞).
The output values, f(x), can take any real number as well. Therefore, the range of the function is also all real numbers, or (-∞, +∞).
E. To find x when f(x) = 0 using the graph, we locate the y-axis (the vertical axis on the coordinate plane) and find the point where the graph intersect it. The x-coordinate of this point will be the value of x when f(x) = 0.
From the graph, we can see that when f(x) = 0, the corresponding x-coordinate is x = 2. We find this by locating the point where the graph intersects the y-axis, which is the point (2, 0).
Therefore, x = 2 when f(x) = 0.
F. To find f(x) when x = 3 using the graph, we locate the x-axis (the horizontal axis on the coordinate plane) and find the point where the graph intersects it. The y-coordinate of this point will be the value of f(x) when x = 3.
From the graph, we can see that when x = 3, the corresponding y-coordinate is f(3) = -4. We find this by locating the point where the graph intersects the x-axis, which is the point (3, -4).
Therefore, when x = 3, f(x) = -4.
A. To find f(-2), you need to substitute -2 into the equation for x:
f(-2) = 8 - 4(-2)
Simplifying the equation:
f(-2) = 8 + 8
Therefore, f(-2) = 16.
B. To find the value of x when f(x) = 8, you need to substitute 8 into the equation for f(x):
8 = 8 - 4x
Subtracting 8 from both sides of the equation:
0 = -4x
Dividing both sides of the equation by -4:
0/-4 = x
Therefore, x = 0.
C. To graph the function f(x) = 8 - 4x, you can follow these steps:
1. Create a coordinate system on a piece of graph paper or using a graphing software.
2. Mark the x-axis and the y-axis.
3. Choose a range of x values that you want to plot on the graph.
4. Substitute each chosen x value into the equation to calculate its corresponding y value.
5. Plot the points (x, y) on the graph.
6. Connect the points with a straight line.
D. The domain of a function is the set of all valid input values (x values) for the function.
In the given function f(x) = 8 - 4x, there are no restrictions or limitations on the value of x. Therefore, the domain is all real numbers.
The range of a function is the set of all possible output values (y values) for the function.
In the given function f(x) = 8 - 4x, the coefficient of x is -4, indicating that as x increases, f(x) decreases. Similarly, as x decreases, f(x) increases. Therefore, the range is all real numbers.
E. To find the value of x when f(x) = 0 using the graph, locate the point where the graph intersects the x-axis. The x-coordinate of that point represents the value of x when f(x) = 0. In this case, the graph intersects the x-axis at x = 2. So, when f(x) = 0, x = 2.
F. To find f(x) when x = 3 using the graph, locate the point on the graph where the value of x is 3. Then, locate the corresponding y-coordinate at that point. In this case, when x = 3, the graph has a point at (3, -4). So, when x = 3, f(x) = -4.