5. C
6. either b or d
(not 100% sure)
6. either b or d
(not 100% sure)
Which statement is true about f(x)-2/3lx+4l-6?
2 answers:
1) Taking in account that the function is f(x)= -(2/3) |x+4|-6, I enclose a file with the graph.
That helps you to conclude:
a) The graph of f(x) has a vertex on (-4, -6)
b) When you multiply a function times 2/3 it is vertically compressed which is equivalent to horizontally streched.
c) The graph of f(x) opens downward
d) The domain of f(x) is all the real values (the absolute function accepts any value of x either positive or negative)
Answer: the graph of f(x) is horizontally stretched.
That helps you to conclude:
a) The graph of f(x) has a vertex on (-4, -6)
b) When you multiply a function times 2/3 it is vertically compressed which is equivalent to horizontally streched.
c) The graph of f(x) opens downward
d) The domain of f(x) is all the real values (the absolute function accepts any value of x either positive or negative)
Answer: the graph of f(x) is horizontally stretched.
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Answer:
(-1, -1)
Step-by-step explanation:
To solve a system of equations by graphing, first graph the lines. Then, find where the two lines hit each other. This is called the "point of intersection", which is the solution. Mark this point's coordinates as an ordered pair (x, y) for your answer.
The equations are in slope-intercept form y = mx + b.
"x" and "y" are points on the line.
"m" is the slope, which equals to .
"b" is the y-intercept, where a line hits the y-axis.
For y = 4x + 3 (blue):
b = 3. This first point is at "3", on the y-axis. Draw a dot there. Use the slope to get another point.
m = 4. Write it as a fraction to get the rise and run values.
From your first point, "rise" (go up) 4 squares, and "run" (go right) 1 squares. Put a dot here too.
Now, you can <u>connect the two points</u> to form a straight line. Remember to put arrows at the ends of the line.
For y = -x - 2 (red):
b = -2. This first point is at "-2", on the y-axis. Put a dot here.
Let's find the next point using the slope.
m = -1. Write it as a fraction to get the rise and run values.
From your first point, "rise" -1 squares. This means to go down 1 square because the fraction is negative. "Run" (go right, same as before) 1 square. Draw your second point here.
Now, you can <u>connect the two points</u> to form a straight line. Remember to put arrows on the line again.
Extend the lines (keep making them longer) until they hit each other. Where they meet is the solution of the system.
The solution is (-1, -1).
Answer:
<em>The area of the triangle DEF is 10.</em>
Step-by-step explanation:
<u>Area of a Triangle:</u>
A triangle of base B and height H (both must be perpendicular) has an area of:
The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.
This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:
B=3-(-2)=3+2=5
Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.
H=2-(-2)=4
With these two values, we calculate the area:
The area of the triangle DEF is 10.
