Answer:
c) 3 units
d) g(x) - f(x) = x² + 2x
e) (-∞, -2] ∪ [0, ∞)
Step-by-step explanation:
<h3><u>Part (c)</u></h3>
To calculate the length of FC, first find the coordinates of point C.
The y-value of point C is zero since this is where the function f(x) intercepts the x-axis. Therefore, set f(x) to zero and solve for x:
As point C has a <u>positive</u> x-value, C = (1, 0).
To find point F, substitute the x-value of point C into g(x):
⇒ F = (1, 3).
Length FC is the <u>difference</u> in the y-value of points C and F:
<h3><u>Part (d)</u></h3>
Given functions:
Therefore:
<h3><u>Part (e)</u></h3>
The values of x for which g(x) ≥ f(x) are where the line of g(x) is above the curve of f(x):
Point A is the <u>y-intercept</u> of both functions, therefore the x-value of point A is 0.
To find the x-value of point E, equate the two functions and solve for x:
As the x-value of point E is negative ⇒ x = -2.
Therefore, the values of x for which g(x) ≥ f(x) are:
- <u>Solution</u>: x ≤ -2 or x ≥ 0
- <u>Interval notation</u>: (-∞, -2] ∪ [0, ∞)
Answer: 20 feet.
Step-by-step explanation:
Observe the right triangle attached.
You need to find the value of "x".
Then, you can use the Pythagorean Theorem:
Where "a" is the hypotenuse of the triangle, and "b" and "c" are the legs.
In this case, you can identify that:
Substitute these values into :
Now, you need to solve for x to find how far up the wall the top of the ladder reaches. Then you get:
<span>a function exists when there is only one output for any given input</span>
Answer:
- a. g(-1)=-16
- b. g(2)=2
- e. f(2)=4
Step-by-step explanation:
When numerous function evaluations are involved, it is convenient to let a calculator or spreadsheet do them.
The function values that match your answer list are shown above.