Exploring Domain and Range Functions

• Linear

• Quadratic

• Exponential

• Logarithmic

Answer explanation

The function f(x) = x^2 + 3x + 2 is a polynomial of degree 2, which defines a quadratic function. Quadratic functions have the general form ax^2 + bx + c, where a, b, and c are constants.

Answer explanation

The function f(x) = 1/(x-2) is undefined at x=2, where the denominator becomes zero. Therefore, the domain excludes 2, resulting in (-∞, 2) ∪ (2, ∞) as the correct choice.

• 9

• -9

• 7

• -7

Answer explanation

To evaluate f(x) at x = -3, we use the first case since -3 < 0. Thus, f(-3) = (-3)^2 = 9. The correct answer is 9.

Answer explanation

The function f(x) = √x is defined for x ≥ 0, producing outputs from 0 to ∞. Thus, the range is [0, ∞), as it includes all non-negative real numbers.

• Linear

• Quadratic

• Exponential

• Logarithmic

Answer explanation

The function f(x) = 3^x is an exponential function because it has a constant base (3) raised to the variable exponent (x). This distinguishes it from linear, quadratic, and logarithmic functions.

Answer explanation

The function f(x) = |x| is defined for all real numbers. Therefore, the domain is all real numbers, which is represented as (-∞, ∞). This is the correct choice.

• 4

• 3

• 5

• 2

Answer explanation

To evaluate f(x) at x = 2, we use the second case since 2 >= 1. Thus, f(2) = 2^2 = 4. The correct answer is 4.

Answer explanation

The function f(x) = x^2 outputs values starting from 0 (when x=0) and goes to infinity as x increases or decreases. Therefore, the range is [0, ∞), which includes all non-negative real numbers.

• Linear

• Quadratic

• Exponential

• Logarithmic

Answer explanation

The function f(x) = log(x) is a logarithmic function, characterized by its inverse relationship to exponential functions. It is not linear or quadratic, as those involve polynomial expressions.

Answer explanation

The function f(x) = 1/x is undefined at x = 0, as division by zero is not allowed. Therefore, the domain excludes 0, resulting in (-∞, 0) ∪ (0, ∞) as the correct choice.