algebra EOC10

Front

What is the rate of change of a linear function?

Back

The rate of change of a linear function is the slope, which represents the change in y for a unit change in x. It can be calculated as \( \frac{\Delta y}{\Delta x} \).

Front

How do you find the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For example, in a quadratic function representing a real-world scenario, the domain may be limited to non-negative values.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form \( y = ax^2 + bx + c \). Its graph is a parabola.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It represents the maximum or minimum value of the quadratic function.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It represents the value of y when x = 0.

Front

How do you determine the slope from a graph?

Back

The slope can be determined by selecting two points on the line and using the formula \( \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \).

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form \( f(x) = a \cdot b^x \), where \( a \) is a constant, \( b \) is the base, and \( x \) is the exponent.

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if, as x increases, y also increases. It is decreasing if, as x increases, y decreases.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.