Functions and Relations in Algebra Class 10

piecewise

True (A)

P100

<p>Multiplication = Multiply numerators together to get the new numerator. Division = Multiply denominators together to get the new denominator.</p> Signup and view all the answers

<p>Divide the numerator of the first fraction by the denominator of the second fraction. (B)</p> Signup and view all the answers

<p>To identify common factors for simplification.</p> Signup and view all the answers

<p>cancelling</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>15 (C)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>Cancel out common factors in the numerator and denominator.</p> Signup and view all the answers

<p>f+g</p> Signup and view all the answers

<p>Sum = (f-g)(x) Difference = (f+g)(x) Product = (f g)(x) Quotient = (f/g)(x)</p> Signup and view all the answers

<p>You multiply the dividend by the reciprocal of the divisor. (D)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>The least common denominator (LCD).</p> Signup and view all the answers

<p>y = 0.5^x (A)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>The value is included in the solution set. (C)</p> Signup and view all the answers

<p>{x∈R | x ≤ 0}</p> Signup and view all the answers

<p>one-to-one</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>Rewrite as a single rational expression, identify x values that are zero or undefined, determine intervals and signs.</p> Signup and view all the answers

<p>f(x) = 5x^2 = None of these 2 ≥ (1/2)^x = Exponential inequality 74x = y = Exponential function 4(10^x - 2) = 500 = Exponential equation</p> Signup and view all the answers

<p>7 &lt; 14^x + 3 (A)</p> Signup and view all the answers

<p>convenient</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Shaded Circle = Indicates that a value is included in the solution set. Hollow Circle = Indicates that a value is excluded from the solution set. Interval = A range between two points on the number line. Test Point = A value chosen from an interval to determine the sign of the expression.</p> Signup and view all the answers

<p>Included solutions and excluded values. (A)</p> Signup and view all the answers

<p>5</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>5</p> Signup and view all the answers

<p>f = {(1,2),(2,3),(3,5),(4,7)} (A), h = {(1,3),(2,6),(3,9)} (C)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>A method to determine if a graph represents a function by checking if any vertical line intersects the graph more than once.</p> Signup and view all the answers

<p>most</p> Signup and view all the answers

<p>f = {(1,2),(2,3),(3,5),(4,7)} = Function g = {(1,3),(1,4),(2,5),(2,6),(3,7)} = Not a function h = {(1,3),(2,6),(3,9)} = Function k = {(1,1),(1,2),(2,3)} = Not a function</p> Signup and view all the answers

<p>Graph with a curve intersecting a vertical line more than once (A)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>Relation g is not a function because it has ordered pairs with the same x-value (1) that correspond to different y-values (3 and 4).</p> Signup and view all the answers

<p>Concentration of a drug in the bloodstream (D)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Eliminate denominators by multiplying by the least common denominator.</p> Signup and view all the answers

<p>table</p> Signup and view all the answers

<p>They can be introduced by eliminating denominators. (B)</p> Signup and view all the answers

<p>v(t)=10/t = Represents velocity as a function of time c(t)=5t/(t^2+1) = Represents drug concentration over time 2/x - 3/2x = 1/5 = Example of a rational equation t=1 = Time at which maximum concentration occurs</p> Signup and view all the answers

<p>By analyzing the graph of the concentration function.</p> Signup and view all the answers

<p>LCD</p> Signup and view all the answers

A function representing velocity as a function of time.

Represents the concentration of a drug in the bloodstream over time.

A relationship expressed as a fraction of polynomials.

A display of values for a function at specific points.

Finding values that satisfy an equation involving fractions.

The smallest common multiple of the denominators in an equation.

Solutions that emerge from the equation but don't satisfy the original equation.

Highest level of drug in the bloodstream occurs at a specific time.

Fractions that represent the same value but have different numerators and denominators.

The combined value of two fractions with a common denominator.

Removing the same factors from the numerator and denominator before multiplying or dividing.

To divide two fractions, multiply the first by the reciprocal of the second.

A way to represent mathematical functions, such as f(x), to explain inputs and outputs.

The sum of two functions, represented by (f+g)(x)=f(x)+g(x).

The result when two functions are multiplied together, denoted by (fg)(x) = f(x)g(x).

An inequality that involves a rational expression.

A specific value chosen to determine the sign of a rational function within an interval.

Visual representation indicating included or excluded values of solutions.

Dividing the number line into segments based on solutions and undefined points.

A fraction where the numerator and denominator are polynomials.

Values of x that make the rational expression equal to zero.

A value of x where the rational expression is undefined.

Clearing fractions by multiplying through by the least common denominator.

A rule that relates values from a set (domain) to another set (range).

A special relation where each domain element corresponds to exactly one range value.

A method to determine if a graph represents a function by checking if vertical lines cross the graph at most once.

A pair of values (x,y) representing a relation on the graph.

The set of all possible input values (x-values) for a function.

The set of all possible output values (y-values) of a function.

Visual representations that show how each element of the domain is related to elements of the range.

Using functions to represent and analyze real-world scenarios.

A function of the form f(x) = a^x where a > 0 and a ≠ 1.

An equation where the variable appears as an exponent, like a^x = b.

An inequality that involves an exponential function, like a^x < b.

A term representing cases that don't fit exponential functions or equations.

Exponential functions are one-to-one; if a^x = a^y, then x = y.

Finding the variable in equations of the form a^x = b.

A rapid increase of a quantity, often modeled by an exponential function.

A decline in quantity modeled by an exponential function.

A piecewise function representing the monthly cost of text messaging based on the number of messages sent.

A function defined by multiple sub-functions, each applicable to a specific interval.

The set of all possible input values (x-values) for a function.

The process of simplifying fractions by removing common factors from the numerator and denominator.

Expressing a number as a product of its prime numbers.

The mathematical actions that can be performed with functions, such as addition, subtraction, multiplication, and division.

Functions expressed as a ratio of two polynomials.

To compute the output value of a function for a specific input.