Answer:
1. The minus before the |x| reflects the function in the x-axis. So it will still be V-shaped but instead but refected in the x-axis.
2. The +4 moves the function vertically 4 units upwards.
Step-by-step explanation:
We are given the function f(x) = - |x| +4. We know that the function f(x) = |x| only has positive values, so when x>0 the function is a straight line as in the function f(x) = x. When x<0 the function is also positive, as in the function f(x) = -x. So the graph is V-shaped with the vertex at the origin.
The f(x) = - |x| +4 has two important caracteristics:
1. The minus before the |x| reflects the function in the x-axis. So it will still be V-shaped but instead but refected in the x-axis.
2. The +4 moves the function vertically 4 units upwards.
So the graph of f(x) = - |x| +4 will be V-shaped, reflected in the x-axis and moved 4 units upwards.
Attached you can find the graph
Answer:
The ribbon cost per foot $0.6 per foot
Step-by-step explanation:
Total number of ribbon used = (5.75 + 11.75) = 17.50 feet
17.50 feet of ribbon cost = $10.50
1 foot of ribbon cost = x
Cross Multiply
17.50 × x = 1 foot × $10.50
x = 1 foot × 10.50/17.50
x = $0.6
The ribbon cost per foot $0.6 per foot
y = x² + 3x - 7
y - 5x + 8 → y = 5x - 8
5x - 8 = x² + 3x - 7 <em>substituted "y" in first equation with "5x - 8"</em>
0 = x² - 2x + 1 <em>subtracted 5x and added 8 to both sides</em>
0 = (x -1)(x - 1) <em>factored x² - 2x + 1 </em>
x = 1 <em>solved for "x"</em>
Now plug that "x = 1" into "y = 5x - 8" → y = 5(1) - 8 → y = 5 - 8 → y = -3
Solution is (1, -3) so there is only one solution.
Answer: C
A. the value of the function will approach zero as the value of x gets very large.
b. when x=0, the function is undefined, because 1/x is a fraction and the denominator of a fraction cannot be zero.