Given a integer depending on whether or not it is positive or negative it is always opposite of what it is. For example the opposite of 7 is -7
The slope of the line connecting two points (<em>a</em>, <em>b</em>) and (<em>c</em>, <em>d</em>) is
(<em>d</em> - <em>b</em>) / (<em>c</em> - <em>a</em>)
i.e. the change in the <em>y</em>-coordinate divided by the change in the <em>x</em>-coordinate. For a function <em>y</em> = <em>f(x)</em>, this slope is the slope of the secant line connecting the two points (<em>a</em>, <em>f(a)</em> ) and (<em>c</em>, <em>f(c)</em> ), and has a value of
(<em>f(c)</em> - <em>f(a)</em> ) / (<em>c</em> - <em>a</em>)
Here, we have
<em>f(x)</em> = <em>x</em> ²
so that
<em>f</em> (1) = 1² = 1
<em>f</em> (1.01) = 1.01² = 1.0201
Then the slope of the secant line is
(1.0201 - 1) / (1.01 - 1) = 0.0201 / 0.01 = 2.01
The function that models the graph is given as:
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
The equation shown in the graph represents a piecewise function. Hence:
From the line through the point (-8, 4) and (-2, 2), the equation is f(x) = -(1/3)x + 4/3
From the curve through the point (-2, 2) and (0, 6), the equation is f(x) = -x² + 6
From the line through the point (0, 6) and (4, 6), the equation is f(x) = -6
From the line through the point (4, 6) and (7, 9), the equation is f(x) = x + 2
The function that models the graph is given as:
Find out more on equation at: brainly.com/question/2972832
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