The table of inputs that satisfy the given function is (<em>-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).</em>
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more variables and numbers.
Given the function f(x) = -5(x + 7)
When x = -2; f(-2) = -5(-2 + 7) = -25
When x = -1; f(-1) = -5(-1 + 7) = -30
When x = 0; f(0) = -5(0 + 7) = -35
When x = 1; f(1) = -5(1 + 7) = -40
When x = 2; f(2) = -5(2 + 7) = -45
The table of inputs that satisfy the given function is (<em>-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).</em>
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Use the distance formula:
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Plug in the given coordinates:
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Simplify:
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You can leave it as:
or in decimal form as: 7.2
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Answer:
145
Step-by-step explanation:
x = 2 , y= 5
Putting the values of x and y in the expression
=3(2) (5)^2-5
=3(2)(25)-5
=150 -5
=145
Answer:
i: the domain.
iii: the axis of symmetry.
Step-by-step explanation:
We have the function:
f(x) = x^2
The domain of this function is the set of all real numbers, and the range is:
R: [0, ∞)
(because 0 is the minimum of x^2)
Now we have the transformation:
d(x) = f(x) + 9 = x^2 + 9
Notice that this is only a vertical translation of 9 units, then there is no horizontal movement, then the axis of symmetry does not change.
Also, in d(x) there is no value of x that makes a problem, so the domain is the set of all real numbers, then the domain does not change.
And d(x) = x^2 + 9 has the minimum at x = 0, then the minimum is:
d(0) = 0^2 + 9 = 9
Then the range is:
R: [9, ∞)
Then the range changes.
So we can conclude that the attributes that will be the same for f(x) and d(x) are:
i: the domain.
iii: the axis of symmetry.
Answer:
Step-by-step explanation:
(a) The function ...
can be evaluated for x=-2√2 to get ...
The point (-2√2, 1) is on the graph of f(x).
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(b) Likewise, we can evaluate for x=2:
The point on the graph is (2, 0.8).
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(c) From part (a), we know that f(-2√2) = 1. Since the function is even, this means that f(2√2) = 1. The graph is a maximum at those points, so there are no other values for which f(x) = 1.
The points (±2√2, 1) are on the graph.
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(d) There are no values of x for which f(x) is undefined. The domain is all real numbers.
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(e) The only x-intercept is at the origin, (0, 0). The x-axis is a horizontal asymptote.
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(f) The only y-intercept is at the origin, (0, 0).
