What is the difference between a function and a relation?

A function is a specific type of relation where each input (x-value) has exactly one output (y-value). A relation can have multiple outputs for a single input.

What does it mean for a function to be decreasing?

A function is decreasing if, as $$x$$ increases, $$y$$ decreases. This means the graph of the function slopes downward from left to right.

What is a y-intercept?

The y-intercept is the point where a graph intersects the y-axis. It is represented as $$(0, b)$$ , where $$b$$ is the value of $$y$$ when $$x = 0$$ .

How can you identify a quadratic function from its graph?

A quadratic function can be identified by its U-shaped graph (parabola) that opens upwards or downwards.

What is the general shape of an exponential function's graph?

The graph of an exponential function increases rapidly (or decreases rapidly) and has a characteristic curve that approaches the x-axis but never touches it.

What is the significance of the coefficients in a quadratic function?

The coefficient $$a$$ determines the direction of the parabola (upward or downward), while $$b$$ affects the position of the vertex and the axis of symmetry.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula $$x = -\frac{b}{2a}$$ .

How do you determine if a function is linear, quadratic, or exponential?

To determine the type of function, analyze its equation or graph: a linear function has a constant rate of change, a quadratic function has a variable rate of change (parabola), and an exponential function grows or decays at a constant percentage rate.

Algebra 1 SLO (Function Families) Flashcards

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FLASHCARD QUESTION

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What is a linear function?

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