1 - 4 please help !!!!
1 answer:
We can use the slope formula for each of these.
1. 5 - 1 / 4 - 2
4 / 2
2
The slope is 2, and it is rising because it is positive.
2. -5 - 0 / 3 - (-1)
-5 / 4
The slope is -5/4, and it is falling because it is negative.
3. 1 - 1 / -3 - 2
0 / -5
0
The slope is 0, and it is a horizontal line. The value of y is not changing per value of x.
4. -5 - 2 / -1 - (-1)
-7 / 0
Undefined
The slope is undefined because it fails the vertical line test.
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Answer:
- turning point: (0, -1)
- domain, range: all real numbers
- x-intercept: (1/27, 0)
- y-intercept: (0, -1)
- transformations: vertical expansion by a factor of 3; translation down 1
Step-by-step explanation:
There are a couple of transformations that may be of interest:
g(x) = k·f(x) . . . . vertical scaling by a factor of k
g(x) = f(x) +k . . . vertical translation by k units (up)
g(x) = f(x -k) . . . horizontal translation by k units (right); <em>not used here</em>
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Unlike the square root function, which is undefined for negative values, the cube root function is defined for all real numbers. Its domain and range are all real numbers.
The turning point of a cube-root function is the origin. Here, that has been translated down 1 unit, so it is (0, -1). That is also the y-intercept.
The x-intercept is the value of x where g(x)=0:
0 = 3∛x -1
1 = 3∛x
1/3 = ∛x
(1/3)³ = x = 1/27
The x-intercept is (1/27, 0).
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<u>Transformations</u>
As we discussed above, the addition of -1 to the parent function causes it to be translated down 1 unit.
The multiplication of the parent function by 3 causes it to be vertically expanded by a factor of 3.
