Precalculus Functions and Graphs 4th. Edition by Mark Dugopolski | 9780321789433 | 0321789431 | Holooly

Precalculus Functions and Graphs

535 SOLVED PROBLEMS

Question: B.4.6

Factoring differences and sums of two cubes Factor each polynomial. a. x³ – 27 b. 8w^6 + 125z³ ...

Verified Answer:

a. Since

x^{3}-27=x^{3}-3^{3}

, we ...

Question: B.4.5

Factoring the special products Factor each polynomial. a. 4x² – 1 b. x² – 6x + 9 c. 9y² + 30y + 25 ...

Verified Answer:

a. 4x² - 1 = (2x)² - 1² Recognize t...

Question: 10.4.6

Rotation of axes for an ellipse Use rotation of axes to write 21x² – 10√3xy + 31y² = 144 in the standard form of an ellipse and sketch its graph. ...

Verified Answer:

We have

A=21, B=-10 \sqrt{3}

, an...

Question: 10.4.5

Rotation of axes for a hyperbola Use rotation of axes to write y = 1/x in the standard form for a hyperbola. ...

Verified Answer:

Since y = 1/x is equivalent to xy - 1 = 0, we have...

Question: 10.4.3

Relating the coordinates Suppose that the x- and y-axes are rotated through the angle π/3. If the point P has coordinates (2, 5) in the xy-system, then what are the coordinates of P in the x’y’-system? ...

Verified Answer:

Use the rotation equations

x^{\prime}=x \c...

Question: 10.3.3

Graphing a hyperbola centered at (h, k) Determine the foci and equations of the asymptotes, and sketch the graph of (x – 2)²/9 – (y + 1)²/4 = 1. ...

Verified Answer:

The graph that we seek is the graph of

\fr...

Question: 10.3.2

Graphing a hyperbola opening up and down Determine the foci and the equations of the asymptotes, and sketch the graph of 4y² – 9x² = 36. ...

Verified Answer:

Divide each side of the equation by 36 to get the ...

Question: 10.2.5

Finding the equation for a circle Write the equation for the circle that has center (4, 5) and passes through (-1, 2). ...

Verified Answer:

The radius is the distance from (4, 5) to (-1, 2):...

Question: 10.2.4

Graphing an ellipse centered at (h, k) Sketch the graph and identify the foci of the ellipse (x – 3)²/25 + (y + 1)²/9 = 1. ...

Verified Answer:

The graph of this equation is a translation of the...

Question: 10.2.2

Graphing an ellipse with foci on the x-axis Sketch the graph and identify the foci of the ellipse x²/9 + y²/4 = 1. ...

Verified Answer:

To sketch the ellipse, we find the x-intercepts an...

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