Algebra Functions Quiz: Test Your Knowledge of Graphs

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Questions and Answers

Which type of function can be represented as a straight line?

Discontinuous function
Step function
Continuous function (correct)
Non-linear function

What is the end behavior of a graph of a quadratic equation with a positive leading coefficient?

Rising on both ends (correct)
Falling on the left end and rising on the right end
Falling on both ends
Rising on the left end and falling on the right end

What is the slope of a line parallel to the line with equation $3x - 4y = 8$?

$-3/2$
$3/4$ (correct)
$3/2$
$-3/4$

In a system of equations, what does it mean if there are no solutions?

The system is inconsistent (C) Signup and view all the answers

Which type of function can be represented by a graph that does not have any breaks or holes?

Non-linear function (D) Signup and view all the answers

What is the y-intercept of the line with equation $2x - 3y = 6$?

$(0, 3)$ (B) Signup and view all the answers

In a system of 3 equations and 3 unknowns, how many solutions are possible?

One solution (C) Signup and view all the answers

What is the discriminant of a quadratic equation used to determine?

The number of solutions and their nature (A) Signup and view all the answers

What type of equation can be represented by a graph that forms a U-shaped curve?

Quadratic equation (B) Signup and view all the answers

Match the following functions with their characteristics:

Continuous function = Can be graphed without lifting the pencil Linear function = Graph is a straight line Piecewise function = Defined by different equations for different intervals Quadratic function = Graph is a parabola Signup and view all the answers

Match the following equations with their graph characteristics:

Graph a line = Represents a straight line Graph a quadratic inequality = Represents a U-shaped curve with shading for inequality Graph a linear inequality = Represents a shaded region on either side of a line Graph a parabola = Represents a U-shaped curve Signup and view all the answers

Match the following equations with their solutions methods:

Solve an equation = Find the value(s) of the variable that make the equation true Solve an inequality = Find the range of values for which the inequality is true Solve an absolute value equation = Find the values that satisfy the equation and its absolute value Simplify complex numbers with all operations = Perform arithmetic operations on complex numbers Signup and view all the answers

Match the following systems with their characteristics:

Solve a system of equations = Find the common solution(s) to two or more equations Solve a system of 3 equations and 3 unknowns = Find the values of three unknowns that satisfy three equations simultaneously Know the types of systems of equations = Understand different classifications based on their solutions Given a graph, determine the linear inequalities = Interpret and write inequalities based on graph regions Signup and view all the answers

Match the following quadratic equation forms with their descriptions:

Write a quadratic equation in vertex form = Represent a parabola using its vertex and transformations Find the discriminant and determine the type and number of solutions = Identify nature of solutions based on discriminant value Projectile problem = Real-life application involving parabolic motion Solve quadratic equations by factoring = Use factorization to find roots/solutions of quadratic equations Signup and view all the answers

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Study Notes

Linear Functions

A linear function can be represented as a straight line.

Quadratic Equations

The end behavior of a graph of a quadratic equation with a positive leading coefficient is that the graph opens upward.
A quadratic equation can be represented by a graph that forms a U-shaped curve.

Slope

The slope of a line parallel to the line with equation $3x - 4y = 8$ is $\frac{3}{4}$.

Systems of Equations

If there are no solutions in a system of equations, it means that the lines are parallel and do not intersect.
In a system of 3 equations and 3 unknowns, there are three possible solutions: one unique solution, no solution, or infinitely many solutions.

Graph Characteristics

A graph that does not have any breaks or holes represents a continuous function.

Y-Intercept

The y-intercept of the line with equation $2x - 3y = 6$ is 2.

Discriminant

The discriminant of a quadratic equation is used to determine the number of solutions.

Function Characteristics

Match the following functions with their characteristics:
- Linear functions: can be represented as a straight line
- Quadratic functions: can be represented by a graph that forms a U-shaped curve
- Continuous functions: can be represented by a graph that does not have any breaks or holes

Equation Characteristics

Match the following equations with their graph characteristics:
- Linear equations: straight line
- Quadratic equations: U-shaped curve

Solution Methods

Match the following equations with their solutions methods:
- Linear equations: substitution, elimination, or graphing
- Quadratic equations: factoring, quadratic formula, or graphing

System Characteristics

Match the following systems with their characteristics:
- System of 2 equations and 2 unknowns: one unique solution, no solution, or infinitely many solutions
- System of 3 equations and 3 unknowns: one unique solution, no solution, or infinitely many solutions

Quadratic Equation Forms

Match the following quadratic equation forms with their descriptions:
- Standard form: $ax^2 + bx + c = 0$
- Vertex form: $a(x - h)^2 + k = 0$
- Factored form: $a(x - r)(x - s) = 0$

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