When x = 1:
1³ + 1 - 3 = -1
When x = 2:
2³ + 2 - 3 = 7
Since f(x) = x³ + x - 3 is continuous, it follows from the intermediate value theorem that for some c in the interval (1, 2), we have f(c) = 0, since f(1) < 0 < f(2).
Answer:
it should be (5,4)
Step-by-step explanation:
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Answer: Hello mate!
we have the function y = f(x) and we want to see how the next changes affect the graph of it:
a) y = 5f(x)
this is a "dilatation" in the y-axis, this means that the graph is 5 times higher than the original graph.
b) y = f(x − 4)
Now we have y = f(0) when x = 4, so here we have the whole graph translated to the right by 4 units
c) y = −2f(x)
This case is similar to the case in a, here we have dilatation of 2 units, but also the points where before the graph was positive, now is negative, and where the graph was negative, now is positive.
So we also have a reflection over the x-axis
d) y = f(3x)
Now, in the point x = 1, we have the value of y = f(3), this means that the value of y = f(1) is in between the x values of 0 and 1, then this is a contraction in the x-axis by 3 times.
e. y = 2f(x) − 5
Ok, here we have two things.
First, you can see another dilatation in the y-axis, but here we also have a subtraction of a constant, this means that the graph is dilated two times in the y-axis, and is translated by -5 units in the y-axis ( translated down by 5 units)
its two ways gather all the relevant information first or throw all the non relevant information out first
