MAT 115 Exam 2024/25
pass grantee
absolute value - ANSWERSa given number's distance from zero
Properties of |X| - ANSWERSIf x > 0, then |x| = x
If x < 0, then |x| = -x
For real numbers A and B, an equation of the form |A| = B, with B ≥ 0, will have
solutions when: - ANSWERSA = B and A = -B
If B < 0, what solution(s) will satisfy the equation |A| = B - ANSWERSIt has no solutions
An absolute value equation in the form of |ax + b| = c has the following properties: -
ANSWERSIf c < 0, |ax + b| = c has no solution
If c = 0, |ax + b| = c has one solution
If c > 0, |ax + b| = c has two solutions
How to solve an absolute value equation - ANSWERSIsolate the absolute value
expression on one side of the equal sign
If c > 0, write and solve two equations: ax + b = c and ax + b = -c
Interval notation can be indicated with - ANSWERSParentheses and/or brackets
With interval notation, parentheses indicate solutions... - ANSWERSgreater or less
than the given number in relation to x
a solution set including all real numbers, negative and positive
How is infinity/negative infinity represented in interval notation? - ANSWERSUse
parentheses
With interval notation, brackets represent solutions that are? - ANSWERSGreater than
or equal to/less than or equal to the given number in relation to x
An interval is - ANSWERSa set of numbers in which a solution falls
"All real numbers between a and b, but not including a or b" in Interval Notion looks
like: - ANSWERS(a,b)
, "All real numbers greater than a, but not including a" in Interval Notation looks like: -
ANSWERS(a, ∞)
All real numbers less than b, but not including b in Interval Notion looks like: -
ANSWERS(-∞,b)
"All real numbers greater than a, including a" in Interval Notation looks like: -
ANSWERS[a, ∞)
"All real numbers less than b, including b" in Interval Notation looks like: -
ANSWERS(−∞, b]
"All real numbers between a and b, including a" in Interval Notation looks like: -
ANSWERS[a,b)
"All real numbers between a and b, including b" in Interval Notation looks like: -
ANSWERS(a, b]
"All real numbers between a and b, including a and b" in Interval Notation looks like: -
ANSWERS[a,b]
"All real numbers less than a or greater than b" in Interval Notation looks like: -
ANSWERS(-∞,a) U (b, ∞)
"All real numbers" in interval notation looks like: - ANSWERS(-∞, ∞)
We think about absolute value as... - ANSWERSThe distance from one number to
another
When representing an inequality on a number line, what determines whether the circle
will be open or closed? - ANSWERSThe symbol being used
What does drawing an open circle on a value represent on a number line? -
ANSWERSThe number is not included in the solution set
What does drawing an closed circle on a value represent on a number line? -
ANSWERSThe number is included in the solution set
For interval notation, If "x" is greater than any given number, that number: -
ANSWERSwill be placed first in the left-hand column (x column)
For interval notation, If "x" is less than any given number, that number: - ANSWERSwill
be placed second in the right-hand column (y column)
The [blank] sign should be placed before the infinity sign when "x" is... - ANSWERSThe
negative sign; less than a given number
pass grantee
absolute value - ANSWERSa given number's distance from zero
Properties of |X| - ANSWERSIf x > 0, then |x| = x
If x < 0, then |x| = -x
For real numbers A and B, an equation of the form |A| = B, with B ≥ 0, will have
solutions when: - ANSWERSA = B and A = -B
If B < 0, what solution(s) will satisfy the equation |A| = B - ANSWERSIt has no solutions
An absolute value equation in the form of |ax + b| = c has the following properties: -
ANSWERSIf c < 0, |ax + b| = c has no solution
If c = 0, |ax + b| = c has one solution
If c > 0, |ax + b| = c has two solutions
How to solve an absolute value equation - ANSWERSIsolate the absolute value
expression on one side of the equal sign
If c > 0, write and solve two equations: ax + b = c and ax + b = -c
Interval notation can be indicated with - ANSWERSParentheses and/or brackets
With interval notation, parentheses indicate solutions... - ANSWERSgreater or less
than the given number in relation to x
a solution set including all real numbers, negative and positive
How is infinity/negative infinity represented in interval notation? - ANSWERSUse
parentheses
With interval notation, brackets represent solutions that are? - ANSWERSGreater than
or equal to/less than or equal to the given number in relation to x
An interval is - ANSWERSa set of numbers in which a solution falls
"All real numbers between a and b, but not including a or b" in Interval Notion looks
like: - ANSWERS(a,b)
, "All real numbers greater than a, but not including a" in Interval Notation looks like: -
ANSWERS(a, ∞)
All real numbers less than b, but not including b in Interval Notion looks like: -
ANSWERS(-∞,b)
"All real numbers greater than a, including a" in Interval Notation looks like: -
ANSWERS[a, ∞)
"All real numbers less than b, including b" in Interval Notation looks like: -
ANSWERS(−∞, b]
"All real numbers between a and b, including a" in Interval Notation looks like: -
ANSWERS[a,b)
"All real numbers between a and b, including b" in Interval Notation looks like: -
ANSWERS(a, b]
"All real numbers between a and b, including a and b" in Interval Notation looks like: -
ANSWERS[a,b]
"All real numbers less than a or greater than b" in Interval Notation looks like: -
ANSWERS(-∞,a) U (b, ∞)
"All real numbers" in interval notation looks like: - ANSWERS(-∞, ∞)
We think about absolute value as... - ANSWERSThe distance from one number to
another
When representing an inequality on a number line, what determines whether the circle
will be open or closed? - ANSWERSThe symbol being used
What does drawing an open circle on a value represent on a number line? -
ANSWERSThe number is not included in the solution set
What does drawing an closed circle on a value represent on a number line? -
ANSWERSThe number is included in the solution set
For interval notation, If "x" is greater than any given number, that number: -
ANSWERSwill be placed first in the left-hand column (x column)
For interval notation, If "x" is less than any given number, that number: - ANSWERSwill
be placed second in the right-hand column (y column)
The [blank] sign should be placed before the infinity sign when "x" is... - ANSWERSThe
negative sign; less than a given number
