Question 1

What is the largest possible area for a rectangle with a perimeter of 40 cm?

Accepted Answer

A)  400 cm 2  
B)  100 cm 2  
C)  90 cm 2  
D)  130 cm 2  
E)  150 cm 2  
A)  400 cm 2  
B)  100 cm 2  
C)  90 cm 2  
D)  130 cm 2  
E)  150 cm 2

Question 2

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. $y = - \frac { 3 } { x - 4 }$

Accepted Answer

A)  no x-intercepts; y-intercept: $- \frac { 3 } { 4 }$ ; vertical asymptote: x = - 4; horizontal asymptote: y = 0;   
B)  no x-intercepts; y-intercept: $\frac { 4 } { 3 }$ ; vertical asymptote: x = 4; horizontal asymptote: y = 0;   
C)  no x-intercepts; y-intercept: $- \frac { 4 } { 3 }$ ; vertical asymptote: x = 4; horizontal asymptote: y = 0;   
D)  no x-intercepts; y-intercept: $\frac { 3 } { 4 }$ ; vertical asymptote: x = 4; horizontal asymptote: y = 0;   
E)  no x-intercepts; y-intercept: $\frac { 1 } { 4 }$ ; vertical asymptote: x = 4; horizontal asymptote: y = 0;   
A)  no x-intercepts; y-intercept: $- \frac { 3 } { 4 }$ ; vertical asymptote: x = - 4; horizontal asymptote: y = 0;   
B)  no x-intercepts; y-intercept: $\frac { 4 } { 3 }$ ; vertical asymptote: x = 4; horizontal asymptote: y = 0;   
C)  no x-intercepts; y-intercept: $- \frac { 4 } { 3 }$ ; vertical asymptote: x = 4; horizontal asymptote: y = 0;   
D)  no x-intercepts; y-intercept: $\frac { 3 } { 4 }$ ; vertical asymptote: x = 4; horizontal asymptote: y = 0;   
E)  no x-intercepts; y-intercept: $\frac { 1 } { 4 }$ ; vertical asymptote: x = 4; horizontal asymptote: y = 0;

Question 3

Graph the quadratic function. Specify the vertex, axis of symmetry, maximum or minimum value, and intercepts. $s = - \frac { 1 } { 4 } t ^ { 2 } - t - 1$

Accepted Answer

A)  vertex: (- 2, 0); axis of symmetry: t = - 2; maximum value: 0; t-intercept: - 2; s-intercept: -1.   
B)  vertex: (- 2, 0); axis of symmetry: t = - 2; minimum value: 0; t-intercept: - 2; s-intercept: 1.   
C)  vertex: (2, 0); axis of symmetry: t = 2; maximum value: 0; t-intercept: 2; s-intercept: -1.   
D)  vertex: (0,1); axis of symmetry: t = 0; maximum value: 1; t-intercept: $\pm 2$ ; s-intercept: 1.   
E)  vertex: (0, 2);axis of symmetry: t = 0; maximum value: 2; t-intercept: $\pm \sqrt { 8 }$ ;s-intercept: 2.   
A)  vertex: (- 2, 0); axis of symmetry: t = - 2; maximum value: 0; t-intercept: - 2; s-intercept: -1.   
B)  vertex: (- 2, 0); axis of symmetry: t = - 2; minimum value: 0; t-intercept: - 2; s-intercept: 1.   
C)  vertex: (2, 0); axis of symmetry: t = 2; maximum value: 0; t-intercept: 2; s-intercept: -1.   
D)  vertex: (0,1); axis of symmetry: t = 0; maximum value: 1; t-intercept: $\pm 2$ ; s-intercept: 1.   
E)  vertex: (0, 2);axis of symmetry: t = 0; maximum value: 2; t-intercept: $\pm \sqrt { 8 }$ ;s-intercept: 2.

Question 4

Two points A and B move along the x-axis. After t sec, their positions are given by the equations A: $\quad x = 4 t + 120$
B: $\quad x = 30 t - 36$ At what time t do A and B have the same x-coordinate?

Accepted Answer

A)  7 sec 
B)  6 sec 
C)  5 sec 
A)  7 sec 
B)  6 sec 
C)  5 sec

Question 5

For the following figure, express the length AB as a function of x. (Hint: Note the similar triangles.)

Accepted Answer

A)  $A B ( x ) = \frac { ( x + 2 ) \sqrt { x ^ { 2 } + 9 } } { x ^ { 2 } }$ 
B)  $A B ( x ) = \frac { ( x + 2 ) \sqrt { x ^ { 2 } + 9 } } { x }$ 
C)  $A B ( x ) = \frac { ( x + 3 ) \sqrt { x + 4 } } { x }$ 
D)  $A B ( x ) = \frac { ( x + 3 ) ^ { 2 } ( x + 2 ) } { x }$ 
E)  $A B ( x ) = \frac { ( x + 3 ) \left( x ^ { 2 } + 2 \right) } { x }$ 
A)  $A B ( x ) = \frac { ( x + 2 ) \sqrt { x ^ { 2 } + 9 } } { x ^ { 2 } }$ 
B)  $A B ( x ) = \frac { ( x + 2 ) \sqrt { x ^ { 2 } + 9 } } { x }$ 
C)  $A B ( x ) = \frac { ( x + 3 ) \sqrt { x + 4 } } { x }$ 
D)  $A B ( x ) = \frac { ( x + 3 ) ^ { 2 } ( x + 2 ) } { x }$ 
E)  $A B ( x ) = \frac { ( x + 3 ) \left( x ^ { 2 } + 2 \right) } { x }$

What is the largest possible area for a rectangle with a perimeter of 40 cm?

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. $y = - \frac { 3 } { x - 4 }$

Graph the quadratic function. Specify the vertex, axis of symmetry, maximum or minimum value, and intercepts. $s = - \frac { 1 } { 4 } t ^ { 2 } - t - 1$

Two points A and B move along the x-axis. After t sec, their positions are given by the equations A: $\quad x = 4 t + 120$ B: $\quad x = 30 t - 36$ At what time t do A and B have the same x-coordinate?

For the following figure, express the length AB as a function of x. (Hint: Note the similar triangles.)

Fundamentals

Equations and Inequalities

Functions

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Exam 4: Polynomial and Rational Functions Applications to Optimization

What is the largest possible area for a rectangle with a perimeter of 40 cm?

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. y=−3x−4y = - \frac { 3 } { x - 4 }y=−x−43​

Graph the quadratic function. Specify the vertex, axis of symmetry, maximum or minimum value, and intercepts. s=−14t2−t−1s = - \frac { 1 } { 4 } t ^ { 2 } - t - 1s=−41​t2−t−1

Two points A and B move along the x-axis. After t sec, their positions are given by the equations A: x=4t+120\quad x = 4 t + 120x=4t+120 B: x=30t−36\quad x = 30 t - 36x=30t−36 At what time t do A and B have the same x-coordinate?

For the following figure, express the length AB as a function of x. (Hint: Note the similar triangles.)

Fundamentals

Equations and Inequalities

Functions

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. $y = - \frac { 3 } { x - 4 }$

Graph the quadratic function. Specify the vertex, axis of symmetry, maximum or minimum value, and intercepts. $s = - \frac { 1 } { 4 } t ^ { 2 } - t - 1$

Two points A and B move along the x-axis. After t sec, their positions are given by the equations A: $\quad x = 4 t + 120$ B: $\quad x = 30 t - 36$ At what time t do A and B have the same x-coordinate?