a. The point, (2, 11) is not on the graph of f.
b. The point on the graph is: (-2, 15).
c. The points that are on the graph are: (0, 0) and (0.25, -3).
d. The domain of f are all possible x-values of the function.
e. The y-intercept is -3.
How to Solve a Function?
The x-intercept of a function is the point at which the line intersects the x-axis. At this point, the value of the corresponding y-value is 0. The zeros of a function are the x-intercepts of the function.
The y-intercept, on the other hand, is the value of y when x = 0. This is where the line intercepts the y-axis.
We are given the function, f(x) = 4x² - x - 3, we will use it to answer the given questions as shown below.
a. Substitute x = 2 into f(x) = 4x² - x - 3
f(2) = 4(2²) - 2 - 3 = 27
f(2) = 27, therefore, the point, (2, 11) is not on the graph of f.
b. Substitute x = -2 into f(x) = 4x² - x - 3 to find f(x)
f(-2) = 4(-2²) - (-2) - 3 = 15
f(-2) = 15
The point on the graph is: (-2, 15).
c. Substitute f(x) = -3 into f(x) = 4x² - x - 3
-3 = 4x² - x - 3
0 = 4x² - x - 3 + 3
0 = 4x² - x
Factorize
x = 0, and x = 0.25
The points that are on the graph are: (0, 0) and (0.25, -3).
d. The domain of f are all possible x-values of the function.
e. 4x² - x - 3 = 0
Factorize
x = 1, x = -3/4.
The x-intercepts are, 1 and -3/4.
f. f(0) = 4(0²) - 0 - 3
f(0) = 0 - 0 - 3
f(0) = -3
The y-intercept is -3.
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