Operations on Functions

If f(x) = 3x^2 - 2x + 1 and g(x) = x - 4, what is (f*g)(x)?

• 3x^3 - 14x^2 + 9x - 4

• 3x^3 - 10x^2 + 5x - 4

• 3x^3 - 12x^2 + 8x - 5

• 3x^3 - 16x^2 + 7x - 3

What is the zero-product property?

• If the product of two factors is zero, then both factors must be zero.

• If the product of two factors is zero, then at least one of the factors must be zero.

• The zero-product property only applies to positive numbers.

• The zero-product property states that the sum of two factors is zero.

What is the formula for function multiplication?

• (f*g)(x) = f(x) + g(x)

• (f*g)(x) = f(x) - g(x)

• (f*g)(x) = f(x) * g(x)

• (f*g)(x) = f(x) / g(x)

What is the vertex form of a quadratic function?

• f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

• f(x) = ax^2 + bx + c, where a, b, and c are constants.

• f(x) = a(x + h)^2 + k, where (h, k) is the vertex of the parabola.

• f(x) = a(x - h)^2 - k, where (h, k) is the vertex of the parabola.

If f(x) = x^2 + x and g(x) = 3x + 1, what is the value of f(g(4))?

• 150

• 172

• 182

• 200

What is the significance of the leading coefficient in a polynomial?

• It determines the degree of the polynomial.

• It determines the end behavior of the polynomial function and influences its shape.

• It affects the number of roots the polynomial can have.

• It indicates whether the polynomial is even or odd.

What is the degree of a polynomial?

• The degree of a polynomial is the highest power of the variable in the polynomial expression.

• The degree of a polynomial is the number of terms in the polynomial.

• The degree of a polynomial is the sum of the coefficients of the polynomial.

• The degree of a polynomial is the lowest power of the variable in the polynomial expression.

What is the standard form of a quadratic function?

• f(x) = ax^2 + bx + c, where a, b, and c are constants.

• f(x) = a(x - h)^2 + k, where (h, k) is the vertex.

• f(x) = a(x + b)(x - c), where b and c are roots.

• f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.

If g(x) = 3x + 4 and h(x) = 3x - 1, what is g(h(x))?

• 9x + 1

• 9x + 7

• 6x + 4

• 12x + 3

What is the difference between a polynomial function and a linear function?

• A polynomial function can have multiple terms with varying degrees, while a linear function is a polynomial of degree one, represented as f(x) = mx + b.

• A polynomial function is always a single term, while a linear function can have multiple terms.

• A polynomial function has a constant rate of change, while a linear function does not.

• A polynomial function can only be represented graphically, while a linear function can be represented numerically.