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) just plug in -2 for x
b) set 8-4x = 8 and solve for x
c) http://www.wolframalpha.com/input/?i=plot+y%3D+8-4x
d) set of real numbers for both
e) and f), use the graph I gave you
the domain of all polynomials is all real numbers.
f(x) = 8-4x.
So, for f(-2), replace every x with -1:
f(-2) = 8-4(-2) = 8+8 = 16
To graph the function, you just need two points. You already have (-2,16). So, pick any other value for x (0 is an easy one!) and plot (0,f(0)).
Draw the line between the two points. The rest should be easy.
A. To find f(-2), we substitute -2 for x in the expression f(X)=8-4x:
f(-2) = 8 - 4(-2)
= 8 + 8
= 16
Therefore, f(-2) = 16.
B. To find x when f(x)=8, we substitute 8 for f(x) in the expression f(X)=8-4x:
8 = 8 - 4x
Rearranging the equation:
4x = 0
Dividing both sides by 4:
x = 0
Therefore, x = 0 when f(x) = 8.
C. To graph the function f(X)=8-4x, we plot points on a graph. We can choose a few values of x and find their corresponding values of f(x). Let's choose x = -2, -1, 0, 1, and 2:
For x = -2:
f(-2) = 8 - 4(-2) = 16
For x = -1:
f(-1) = 8 - 4(-1) = 12
For x = 0:
f(0) = 8 - 4(0) = 8
For x = 1:
f(1) = 8 - 4(1) = 4
For x = 2:
f(2) = 8 - 4(2) = 0
Plotting these points on a graph, we can then draw a line connecting them.
D. The domain of the function is all possible values of x for which the function is defined. In this case, there are no restrictions on the value of x, so the domain is (-∞, ∞), which means all real numbers.
The range of the function is all possible values of f(x) that the function can take. In this case, the function is a linear function with a negative slope, and as x increases, f(x) decreases. Therefore, the range of the function is (-∞, 8], meaning all real numbers less than or equal to 8.
E. To find x when f(x) = 0 using the graph, we locate the point where the graph intersects the x-axis. This point represents the x value(s) where f(x) is equal to 0.
From the graph, we can see that the graph intersects the x-axis at x = 2. Therefore, x = 2 when f(x) = 0.
F. To find f(x) when x = 3 using the graph, we locate the point on the graph where x = 3. The y-coordinate of this point represents the value of f(x) when x = 3.
From the graph, we can see that when x = 3, the corresponding value of f(x) is f(3) = 8 - 4(3) = -4. Therefore, f(x) = -4 when x = 3.