Algebraic Representation of Functions Practice Problems

Master algebraic function representation with practice problems on slopes, linear equations, and finding functions from points. Includes step-by-step solutions.

📚What You'll Practice in This Section
  • Calculate slopes of linear functions using two points and the slope formula
  • Find algebraic representations of linear functions given slope and a point
  • Identify slopes directly from linear equations in y = mx + b form
  • Convert table data into algebraic function representations
  • Apply the point-slope formula to create function equations
  • Solve real-world problems using algebraic function models

Understanding Algebraic Representation of a Function

Complete explanation with examples

A function is a connection between an independent variable (X) (X) and a dependent variable (Y) (Y) . The relationship between the variables is called a "correspondence rule".

An algebraic representation of a function is actually a description of the relationship between the dependent variable (Y) (Y) and the independent variable (X) (X) by means of an equation.

The following is the typical structure of a graphical representation:

  • Y=X+3 Y=X+3 , Y=2X−5 Y=2X-5

For example, if the data is that every month, Daniel earns20.000 20.000 dollars.

The algebraic representation will be X X for the number of months Y Y f(X) f (X) for the amount earned. f(x)=20000X f (x) = 20000X

A1 - algebraic representation of a function

Detailed explanation

Practice Algebraic Representation of a Function

Test your knowledge with 12 quizzes

Which of the following equations corresponds to the function represented in the graph?

–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444000

Examples with solutions for Algebraic Representation of a Function

Step-by-step solutions included
Exercise #1

Determine whether the following table represents a function

XY-1015811

Step-by-Step Solution

It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.

In the table, we can observe that there is a constant change in X values, meaning an increase of 1, and a constant change in Y values, meaning an increase of 3

Therefore, according to the rule, the table describes a function.

Answer:

Yes

Video Solution
Exercise #2

Determine whether the data in the following table represent a constant function

XY012348

Step-by-Step Solution

It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.

In the table, we can observe that there is a constant change in X values, meaning an increase of 1, and a non-constant change in Y values - sometimes increasing by 1 and sometimes by 4

Therefore, according to the rule, the table does not describe a function

Answer:

No

Video Solution
Exercise #3

Determine whether the following table represents a constant function:

XY02468-3-3-3-3-3

Step-by-Step Solution

It is important to remember that a constant function describes a situation where, as the X value increases, the Y value remains constant.

In the table, we can see that there is a constant change in the X values, specifically an increase of 2, while the Y value remains constant.

Therefore, the table does indeed describe a constant function.

Answer:

Yes, it does

Video Solution
Exercise #4

Is the given graph a function?

–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–4–4–4–3–3–3–2–2–2–1–1–1111222333000

Step-by-Step Solution

It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y

Let's note that in the graph:

f(0)=2,f(0)=−2 f(0)=2,f(0)=-2

In other words, there are two values for the same number.

Therefore, the graph is not a function.

Answer:

No

Video Solution
Exercise #5

Determine whether the given graph is a function?

–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–4–4–4–3–3–3–2–2–2–1–1–1111222333000

Step-by-Step Solution

It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y

We should note that for every X value found on the graph, there is one and only one corresponding Y value.

Therefore, the graph is indeed a function.

Answer:

Yes

Video Solution

Frequently Asked Questions

Everything you need to know about Algebraic Representation of a Function

What is algebraic representation of a function?

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An algebraic representation of a function is an equation that describes the relationship between the dependent variable (Y) and independent variable (X). For example, Y = 2X + 3 shows that Y equals two times X plus three.

How do you find the slope of a linear function from two points?

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Use the slope formula: m = (y₂ - y₁)/(x₂ - x₁). Substitute the coordinates of your two points and calculate. For points (2,10) and (-5,-4), the slope is (10-(-4))/(2-(-5)) = 14/7 = 2.

What does y = mx + b represent in function notation?

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This is the slope-intercept form where: • m = slope of the line • b = y-intercept (where line crosses y-axis) • x = independent variable • y = dependent variable

How do you write a linear function equation given slope and a point?

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Step 1: Use y = mx + b format. Step 2: Substitute the known slope for m. Step 3: Substitute the point coordinates for x and y. Step 4: Solve for b (y-intercept). Step 5: Write the complete equation.

Can you find function equations from data tables?

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Yes! Choose any two points from the table, calculate the slope using m = (y₂-y₁)/(x₂-x₁), then use one point with the slope in y = mx + b to find b. This gives you the complete algebraic representation.

What's the difference between linear and quadratic function representation?

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Linear functions have the form y = mx + b (first degree, creates straight lines). Quadratic functions have the form y = ax² + bx + c (second degree, creates parabolas). The highest exponent determines the function type.

Why is algebraic representation important in mathematics?

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Algebraic representation allows you to: 1) Express relationships mathematically 2) Make predictions and calculations 3) Solve real-world problems 4) Convert between different function representations 5) Analyze function behavior systematically.

How do you identify the slope from a function equation like y = -3x + 7?

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In the standard form y = mx + b, the coefficient of x is always the slope. So in y = -3x + 7, the slope m = -3. The constant term (+7) is the y-intercept.

More Algebraic Representation of a Function Questions

Click on any question to see the complete solution with step-by-step explanations

Representations of Functions

Match the Function Equation: Analyzing X-Y Values from -3 to 5 Graph to Equation Puzzle: Identify the Matching Function Decipher the Graph's Story: Which Equation Represents This Function? Equation Alignment for Table Mapping of X and Y Identify the Correct Equation: Linking X and Y with Table Data

Continue Your Math Journey

Master Algebraic Representation of a Function first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Ways to Represent a FunctionRepresenting a Function Verbally and with TablesGraphical Representation of a FunctionNotation of a FunctionRate of Change of a FunctionVariation of a FunctionRate of change represented with steps in the graph of the functionRate of change of a function represented graphicallyConstant Rate of ChangeVariable Rate of ChangeRate of Change of a Function Represented by a Table of ValuesFunctions for Seventh GradeIncreasing and Decreasing Intervals (Functions)Increasing functionsDecreasing functionConstant FunctionDecreasing Interval of a functionIncreasing Intervals of a functionDomain of a FunctionIndefinite integralInputing Values into a Function

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems
Creating a table from a verbal description Determine whether the table represents a function Is the graph an example of a function? Matching a graph to a function Matching a graph to a table Matching a table to a function Sketch the Graph from a Verbal Description