Exam 2: Functions and Relations

Choose the one alternative that best completes the statement or answers the question. -For over 20 years, the population of Tressel, Ohio has been increasing linearly according tothe function $P ( t ) = 225 t + 7,000$ where P is the number of residents, and t is years after 1980. Compute P(0) and interpret its Meaning in the context of this problem.

(Multiple Choice)

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Question 181

Evaluate the function for the given value of x. - $f ( x ) = - 2 x , g ( x ) = | x + 2 | , \left( \frac { f } { g } \right) ( - 5 ) = \text { ? }$

(Multiple Choice)

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Question 182

Solve the problem. -Find $f ( 5 )$ for the given function. $f ( x ) = 2$

(Multiple Choice)

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Question 183

Determine if the lines defined by the given equations are parallel, perpendicular, or neither. - -4y=-3x-3 -12x=9y+8

(Multiple Choice)

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Question 184

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } - 8 y + 11 = 0$

(Multiple Choice)

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Question 185

Determine whether the relation defines y as a function of x. -

(Multiple Choice)

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Question 186

Find $\frac { f ( x + h ) - f ( x ) } { h }$ for the given function. - $f ( x ) = x ^ { 2 } + 8 x$

(Multiple Choice)

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Question 187

Use transformations to graph the given function. - $f ( x ) = - ( x + 3 ) ^ { 2 } + 2$

(Multiple Choice)

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Question 188

The graphs of f and g are shown. Find the values for the given values of x, if possible. -a. $( f + g ) ( - 2 )$ b. $\left( \frac { g } { f } \right) ( 1 )$ c. $( g \circ f ) ( 3 )$ $The graphs of f and g are shown. Find the values for the given values of x, if possible. -a. ( f + g ) ( - 2 ) b. \left( \frac { g } { f } \right) ( 1 ) c. ( g \circ f ) ( 3 )$

(Multiple Choice)

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Question 189

Determine if the lines defined by the given equations are parallel, perpendicular, or neither. - -5x-4y=6 x+y=8

(Multiple Choice)

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Question 190

Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. -

(Multiple Choice)

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Question 191

Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y = f(x). - $( - 4 , - 5 ) ; m = 4$

(Multiple Choice)

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Question 192

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Passes through $( 4,1 )$ and the slope is undefined.

(Multiple Choice)

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Question 193

Graph the equations on the standard viewing window. - y= y=|x+3|

(Multiple Choice)

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Question 194

Determine the slope of the line passing through the given points. - $( - 3.4,3.4 )$ and $( - 4.4,2.1 )$ .

(Multiple Choice)

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Question 195

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A set of ordered pairs (x, y) is called a in x and y. The set of x values in the relation is called the of the relation. The set of values is called the range of the relation.

(Short Answer)

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Question 196

Determine whether the relation defines y as a function of x. -

(Multiple Choice)

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Question 197

Write the domain in interval notation. - $z ( a ) = \sqrt { a + 9 }$

(Multiple Choice)

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Question 198

Use the given information about a circle to write an equation of the circle in standard form. -The center is $( - 5 , - 4 )$ and another point on the circle is $( 1,4 )$

(Multiple Choice)

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Question 199

The graphs of f and g are shown. Find the values for the given values of x, if possible. -a. $( h \cdot k ) ( 0 )$ ; b. $\left( \frac { k } { h } \right) ( - 4 )$ ; c. $( k - h ) ( 1 )$ $The graphs of f and g are shown. Find the values for the given values of x, if possible. -a. ( h \cdot k ) ( 0 ) ; b. \left( \frac { k } { h } \right) ( - 4 ) ; c. ( k - h ) ( 1 )$

(Multiple Choice)

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Question 200

Showing 181 - 200 of 380

Evaluate the function for the given value of x. - $f ( x ) = - 2 x , g ( x ) = | x + 2 | , \left( \frac { f } { g } \right) ( - 5 ) = \text { ? }$

Solve the problem. -Find $f ( 5 )$ for the given function. $f ( x ) = 2$

Determine if the lines defined by the given equations are parallel, perpendicular, or neither. - -4y=-3x-3 -12x=9y+8

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } - 8 y + 11 = 0$

Determine whether the relation defines y as a function of x. -

Find $\frac { f ( x + h ) - f ( x ) } { h }$ for the given function. - $f ( x ) = x ^ { 2 } + 8 x$

Use transformations to graph the given function. - $f ( x ) = - ( x + 3 ) ^ { 2 } + 2$

Determine if the lines defined by the given equations are parallel, perpendicular, or neither. - -5x-4y=6 x+y=8

Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. -

Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y = f(x). - $( - 4 , - 5 ) ; m = 4$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Passes through $( 4,1 )$ and the slope is undefined.

Graph the equations on the standard viewing window. - y= y=|x+3|

Determine the slope of the line passing through the given points. - $( - 3.4,3.4 )$ and $( - 4.4,2.1 )$ .

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A set of ordered pairs (x, y) is called a in x and y. The set of x values in the relation is called the of the relation. The set of values is called the range of the relation.

Determine whether the relation defines y as a function of x. -

Write the domain in interval notation. - $z ( a ) = \sqrt { a + 9 }$

Use the given information about a circle to write an equation of the circle in standard form. -The center is $( - 5 , - 4 )$ and another point on the circle is $( 1,4 )$

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

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Exam 2: Functions and Relations

Evaluate the function for the given value of x. - f(x)=−2x,g(x)=∣x+2∣,(fg)(−5)= ? f ( x ) = - 2 x , g ( x ) = | x + 2 | , \left( \frac { f } { g } \right) ( - 5 ) = \text { ? }f(x)=−2x,g(x)=∣x+2∣,(gf​)(−5)= ?

Solve the problem. -Find f(5)f ( 5 )f(5) for the given function. f(x)=2f ( x ) = 2f(x)=2

Determine if the lines defined by the given equations are parallel, perpendicular, or neither. - -4y=-3x-3 -12x=9y+8

Write the given equation in the form (x−h)2+(y−k)2=r2( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }(x−h)2+(y−k)2=r2 . Identify the center and radius. - x2+y2−8y+11=0x ^ { 2 } + y ^ { 2 } - 8 y + 11 = 0x2+y2−8y+11=0

Determine whether the relation defines y as a function of x. -

Find f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​ for the given function. - f(x)=x2+8xf ( x ) = x ^ { 2 } + 8 xf(x)=x2+8x

Use transformations to graph the given function. - f(x)=−(x+3)2+2f ( x ) = - ( x + 3 ) ^ { 2 } + 2f(x)=−(x+3)2+2

The graphs of f and g are shown. Find the values for the given values of x, if possible. -a. (f+g)(−2)( f + g ) ( - 2 )(f+g)(−2) b. (gf)(1)\left( \frac { g } { f } \right) ( 1 )(fg​)(1) c. (g∘f)(3)( g \circ f ) ( 3 )(g∘f)(3)

Determine if the lines defined by the given equations are parallel, perpendicular, or neither. - -5x-4y=6 x+y=8

Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. -

Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y = f(x). - (−4,−5);m=4( - 4 , - 5 ) ; m = 4(−4,−5);m=4

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Passes through (4,1)( 4,1 )(4,1) and the slope is undefined.

Graph the equations on the standard viewing window. - y= y=|x+3|

Determine the slope of the line passing through the given points. - (−3.4,3.4)( - 3.4,3.4 )(−3.4,3.4) and (−4.4,2.1)( - 4.4,2.1 )(−4.4,2.1) .

Determine whether the relation defines y as a function of x. -

Write the domain in interval notation. - z(a)=a+9z ( a ) = \sqrt { a + 9 }z(a)=a+9​

Use the given information about a circle to write an equation of the circle in standard form. -The center is (−5,−4)( - 5 , - 4 )(−5,−4) and another point on the circle is (1,4)( 1,4 )(1,4)

The graphs of f and g are shown. Find the values for the given values of x, if possible. -a. (h⋅k)(0)( h \cdot k ) ( 0 )(h⋅k)(0) ; b. (kh)(−4)\left( \frac { k } { h } \right) ( - 4 )(hk​)(−4) ; c. (k−h)(1)( k - h ) ( 1 )(k−h)(1)

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Evaluate the function for the given value of x. - $f ( x ) = - 2 x , g ( x ) = | x + 2 | , \left( \frac { f } { g } \right) ( - 5 ) = \text { ? }$

Solve the problem. -Find $f ( 5 )$ for the given function. $f ( x ) = 2$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } - 8 y + 11 = 0$

Find $\frac { f ( x + h ) - f ( x ) } { h }$ for the given function. - $f ( x ) = x ^ { 2 } + 8 x$

Use transformations to graph the given function. - $f ( x ) = - ( x + 3 ) ^ { 2 } + 2$

Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y = f(x). - $( - 4 , - 5 ) ; m = 4$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Passes through $( 4,1 )$ and the slope is undefined.

Determine the slope of the line passing through the given points. - $( - 3.4,3.4 )$ and $( - 4.4,2.1 )$ .

Write the domain in interval notation. - $z ( a ) = \sqrt { a + 9 }$

Use the given information about a circle to write an equation of the circle in standard form. -The center is $( - 5 , - 4 )$ and another point on the circle is $( 1,4 )$