Identifying Linear Functions Challenge

Mrs. Pettis teaches students how to identify linear functions using graphs, tables, and equations. She explains that a linear function's graph is a line and uses the vertical line test to determine if a graph is a function. She demonstrates how to check for constant change in tables and outlines the criteria for linear equations, such as having exponents of one and not involving fractions or radicals. The lesson concludes with examples and an invitation to contact her or Mr. A for further assistance.

What is the primary characteristic of a linear function's graph?

• It is a straight line.

• It is a parabola.

• It consists of disconnected points.

• It is a curve.

How do we use the vertical line test to determine if a graph represents a function?

• By checking if the graph touches the vertical line more than once.

• By drawing a horizontal line across the graph.

• By drawing a vertical line and ensuring it only intersects the graph at one point.

• By ensuring the graph does not touch the vertical line.

What is the result of applying the vertical line test to a curve?

• It indicates the curve could be a linear function if it straightens out.

• It shows the curve is not a function.

• It has no significance on the curve's classification.

• It confirms the curve is a linear function.

How does the vertical line test determine if something is a function?

• By intersecting the graph at two points.

• By not intersecting the graph at all.

• By intersecting the graph at multiple points.

• By intersecting the graph at exactly one point.

What indicates a constant change in a table when identifying a linear function?

• The x-values increase by different amounts.

• The x-values are squared.

• The y-values decrease by the same amount.

• The difference between consecutive y-values remains the same.

In a table, if the x-values increase by 1 and the y-values decrease by 3, what can be inferred?

• The relationship is quadratic.

• The relationship is not a function.

• The relationship represents a linear function.

• The relationship is exponential.

Which of the following equations represents a linear function?

• y = x^2 + 3

• y = 2x + 5

• y = x/x + 1

• y = sqrt(x) + 1

Why is the equation y = 2^x not considered a linear function?

• Because it includes a fraction.

• Because x and y are multiplied together.

• Because it includes a square root.

• Because the exponent on x is not one.

What disqualifies an equation from being a linear function?

• The equation is y = 3x + 7.

• The equation includes a term with x^2.

• The equation is y = 12.

• The equation is y = x + 1.

What is a necessary condition for an equation to be considered a linear function?

• The equation must have variables only in the numerator.

• The equation must include a square root.

• The equation must have x and y multiplied together.

• The exponents on the variables must be one.