Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 5}$$?

Accepted Answer

$$x \geq 2.5$$

Question 2

Given the function $$f(x) = x^2$ - 4x + 3$$, which of the following is the correct vertex of its graph?

Accepted Answer

$$(2, -1)$$

Question 3

A car's position is modeled by $$s(t) = 3t^2$ + 2t. $$What is the car's instantaneous velocity at $$t = 4$$ seconds?

Accepted Answer

$$32 m/s$$

Question 4

Which of the following is the correct equation for a circle centered at $$(2, -3)$$ with radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 5

Convert the polar point $$(3, \frac{\pi}{4}) to $$rectangular coordinates.

Accepted Answer

$$(\frac{3}{\sqrt{2}}, \frac{3}{\sqrt{2}})$$

Question 6

Which of the following is the standard form equation of a hyperbola centered at $$(0,0)$$ with transverse axis along the $$x-$$axis, $$a = 2$$, $$b = 3$$?

Accepted Answer

$$\frac{x^2$}{4} - \frac{y^2$}{9} = 1$$

Question 7

A Ferris wheel rotates at a constant angular speed of $$0.5$$ radians per second. What is the linear speed of a seat located $$8$$ meters from the center?

Accepted Answer

$$4 m/s$$

Question 8

Which of the following is the correct equation for the ellipse centered at $$(0,0)$$ with major axis along the $$y-$$axis, $$a = 5$$, $$b = 3$$?

Accepted Answer

$$\frac{x^2$}{9} + \frac{y^2$}{25} = 1$$

Question 9

Given $$f(x) = 2x^3$ - 3x^2$ + x - 5$$, which interval is $$f(x)$$ increasing?

Accepted Answer

$$x \u003e 1$$

Question 10

Which of the following is the correct rectangular equation for the polar equation $$r = 4 \cos 	heta$$?

Accepted Answer

$$x^2$$ + $$y^2 = 4x$

Question 11

A projectile is launched from the ground with an initial velocity of $$v_0 = 20$ m/s at an angle of 30$$^\circ$$ above the horizontal. What is the maximum height reached by the projectile? (Use g = 9.8$ m/s^2$)

Accepted Answer

$$10.2 m$$

Question 12

Which of the following is the correct equation for a parabola with vertex at $$(1,2)$$ opening upward and focus at $$(1,4)$$?

Accepted Answer

$$(x - 1)^2$ = 8(y - 2)$$

Question 13

If $$f(x) = \frac{1}{x - 2}$$, what is the range of $$f(x)$$?

Accepted Answer

$$y 
eq 0$$

Question 14

Which of the following is the correct equation for the tangent line to $$y = x^2$ at x = 3$?

Accepted Answer

$$y = 6x - 9$$

Question 15

A satellite moves in an elliptical orbit with $$a = 10 km $$and $$b = 6 km. $$What is the eccentricity $$e of $$the orbit?

Accepted Answer

$$e = 0.5$$

Question 16

Which of the following is the correct standard form equation for a vertical hyperbola centered at $$(0,0)$$ with $$a = 4$$, $$b = 3$$?

Accepted Answer

$$\frac{y^2$}{16} - \frac{x^2$}{9} = 1$$

Question 17

Given the function $$f(x) = |x - 3|$$, which of the following describes its graph?

Accepted Answer

A V-shaped graph with vertex at $$(3, 0)$$

Question 18

Which of the following is the correct formula for angular speed $$\omega in $$terms of linear speed $$v$$ and radius $$r$$?

Accepted Answer

$$\omega = \frac{v}{r}$$

Question 19

A bridge is designed in the shape of a parabola with vertex at $$(0,0)$$ and passing through $$(10,5). $$What is the equation of the parabola?

Accepted Answer

$$y = \frac{1}{20}x^2$

Precalculus Final Exam Comprehensive Study Guide

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