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For the function
f(x)=x^(2)+4x-1, find the slope of the secant line between
x=-3 and
x=-1.
Answer:

For the function $f(x)=x^{2}+4 x-1$ , find the slope of the secant line between $x=-3$ and $x=-1$ . $\newline$ Answer:

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Complex conjugate theorem

Full solution

Q. For the function

f(x)=x^{2}+4 x-1

, find the slope of the secant line between

x=-3

and

x=-1

.

\newline

Answer:

Slope Formula: To find the slope of the secant line between two points on a function, we use the formula for slope, which is the change in $y$ divided by the change in $x$ (rise over run). This is given by $\frac{f(x_2) - f(x_1)}{x_2 - x_1}$ , where $x_1$ and $x_2$ are the $x$ -values of the two points.
Find $y$ for $x=-3$ : First, we need to find the $y$ -value for $x = -3$ by substituting $-3$ into the function $f(x) = x^2 + 4x - 1$ . This gives us $f(-3) = (-3)^2 + 4(-3) - 1 = 9 - 12 - 1 = -4$ .
Find $y$ for $x=-1$ : Next, we need to find the $y$ -value for $x = -1$ by substituting $-1$ into the function $f(x) = x^2 + 4x - 1$ . This gives us $f(-1) = (-1)^2 + 4(-1) - 1 = 1 - 4 - 1 = -4$ .
Identify Two Points: Now we have the two points on the function: $(-3, f(-3)) = (-3, -4)$ and $(-1, f(-1)) = (-1, -4)$ . We can see that the $y$ -values for both points are the same, which means the slope of the secant line is $0$ because there is no change in $y$ .
Calculate Slope: The slope of the secant line is therefore $(f(-1) - f(-3)) / (-1 - (-3)) = (-4 - (-4)) / (-1 + 3) = 0 / 2 = 0$ .

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