Exercises: Graphing

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Exercises 6.8 Exercises: Graphing

1.

Is the given point on the graph of \(y^2 = x^3 - 10 x + 3\text{?}\) How can you be sure?

\(\displaystyle (3,0)\)

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\(\displaystyle (0,3)\)

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\(\displaystyle (0,\sqrt{3})\)

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\(\displaystyle (\sqrt{3},0)\)

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\(\displaystyle (1,2)\)

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2.

Find an equation for the circle having the points \((-2,4)\) and \((7,9)\) as endpoints of a diameter.

Linear Equations.

3.

Sketch a graph of each equation.

\(\displaystyle x=-4\)

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\(\displaystyle y=3\)

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\(\displaystyle 2y=-1\)

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4.

What is an equation for the \(x\)-axis? What is an equation for the \(y\)-axis?

5.

Find the intercepts of \(4x-7y = 2\) and sketch its graph.

6.

Sketch a graph of \(y - 7 = -2 (x+1)\)

7.

Find a linear equation for the line passing through the points \((5,4)\) and \((-2,3)\text{.}\)

8. Linear Models.

Let \(C\) denote the annual cost in millions of dollars to maintain a computer network \(t\) years since the year 2000 (so that \(t = 0\) corresponds to the year 2000). In 2005, it cost 2 million dollars and, in 2010 it cost 17 million dollars.

At what rate is the cost increasing per year, assuming the rate of increase remains constant?
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Find a linear model for the cost \(C\text{.}\)
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Use your model to predict the cost to maintain the network in 2020.
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9. A Parabola.

Find an equation for the parabola with focus at \(F(0,-1)\) and directrix \(y = 2\text{.}\)