Random Regents Friday

Front

What is the process of simplifying the expression (3x^2 + 4x - 8) + 2(11 - 5x)?

Back

Combine like terms: 3x^2 + 4x - 8 + 22 - 10x = 3x^2 - 6x + 14.

Front

What is the most suitable domain for the function G(m) representing gasoline consumption for traveling m miles?

Back

The domain is nonnegative rational numbers, as distance cannot be negative.

Front

How do you find the equation of a line given a point (6, -3) and a slope of -4/3?

Back

Use the point-slope form: y - y1 = m(x - x1). The equation is 3y = -4x + 15.

Front

What is the degree of the polynomial 2x + x^3 + 5x^2?

Back

The degree is 3, which is the highest exponent in the polynomial.

Front

What is the range of the function f(x) = x^2 + 2x - 5?

Back

The range is greater than or equal to -6, as the vertex of the parabola is at (-1, -6).

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

What does it mean for a function to be linear?

Back

A linear function has a constant rate of change and can be represented by a straight line on a graph.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input has exactly one output.