Linear Functions and Transformations

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Questions and Answers

Which of the following is a key characteristic of a linear function's graph?

  • It forms a straight line. (correct)
  • It forms a curve.
  • It forms a hyperbola.
  • It forms a parabola.

A graph with a discontinuity can be drawn without lifting your pen.

False (B)

What is the significance of intercepts in the graph of a function?

Indicate where the graph intersects the axes

The slope-intercept form of a linear equation is given by $y = mx + b$, where 'm' represents the _______ and 'b' represents the y-intercept.

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

Match the transformation with its effect on a linear function:

<p>Shift = Translation of the graph Stretch = Vertical elongation of the graph Compression = Vertical shortening of the graph Reflection = Flip of the graph over an axis</p> Signup and view all the answers

What does the rate of change measure in the context of a linear function?

<p>How one quantity changes with respect to another. (A)</p> Signup and view all the answers

Solving one-step inequalities involves isolating the variable and does not require flipping the inequality sign when multiplying or dividing by a negative number.

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

Explain what linearity signifies in a function's behavior.

<p>Change in output is proportional to the change in input</p> Signup and view all the answers

_______ of a function implies that there are no sudden jumps, breaks, or gaps in its graph.

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

Which of the following transformations would change the slope of a linear function?

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

Flashcards

Linear Functions

Functions that, when graphed, form a straight line.

Continuous Graphs

Graphs that can be drawn without lifting your pen, indicating no breaks, jumps, or gaps.

Intercepts

The points where a graph crosses the x-axis (x-intercept) and y-axis (y-intercept).

Rate of Change

Measures how much a quantity changes with respect to another quantity, often represented by the slope in linear functions.

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Slope

A measure of the steepness and direction of a line on a graph.

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Slope-Intercept Form

A way to express a linear equation as y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

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Transformations of Linear Functions

Changes to a linear function's graph, including shifts (up, down, left, right), stretches, compressions, and reflections.

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Linearity

The property where the change in output is directly proportional to the change in input.

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Continuity

A function whose graph has no abrupt changes, breaks, or discontinuities.

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