Match each graph to the function listed whose graph most...

Name: Problem 51, Chapter 2: Intermediate Algebra
Uploaded: 2024-01-17T06:04:49-08:00
Duration: 4 min 3 s
Channel: Cheryl Glor
Description: Match each graph to the function listed whose graph most resembles the one given. See Objective 4. (a) Constant function (b) Linear function (c) Square function (d) Cube function (e) Square root function (f) Reciprocal function (g) Absolute value function (h) Cube root function (GRAPH CAN'T COPY)

Match each graph to the function listed whose graph most resembles the one given. See Objective 4. (a) Constant function (b) Linear function (c) Square function (d) Cube function (e) Square root function (f) Reciprocal function (g) Absolute value function (h) Cube root function (GRAPH CAN'T COPY)

Match each graph to the function listed whose graph most resembles the one given. See Objective 4.
(a) Constant function
(b) Linear function
(c) Square function
(d) Cube function
(e) Square root function
(f) Reciprocal function
(g) Absolute value function
(h) Cube root function
(GRAPH CAN'T COPY)

Key Concepts

Reciprocal Function

A reciprocal function is defined by the equation f(x) = 1/x and is characterized by having two distinct branches with vertical and horizontal asymptotes. This function is instrumental in exploring concepts such as undefined points and behavior near zero.

Cube Root Function

A cube root function, written as f(x) = ?x, involves extracting the cube root of the input. Unlike the square root function, it accepts negative inputs as well, resulting in a continuously increasing curve that is smooth and defined over all real numbers.

Absolute Value Function

An absolute value function, represented as f(x) = |x|, outputs the non-negative magnitude of a number regardless of its sign. Its graph typically exhibits a V-shape with a distinct vertex, serving as a useful tool to demonstrate distance and magnitude in algebra.

Cube Function

A cube function involves raising the variable to the third power, and is generally written as f(x) = x³. Its graph features an S-shaped curve with symmetry about the origin, exemplifying how functions can exhibit inflection points and changing concavity.

Constant Function

A constant function is one in which the output value remains unchanged regardless of the input, resulting in a horizontal line on a graph. Its general form is f(x) = c, where c is a constant, and it illustrates scenarios where there is no variation or change over time.

Square Function

A square function, often referred to as a quadratic function when expressed in its standard form, involves the input variable being raised to the power of two. Its graph is a parabola, which is symmetric and either opens upward or downward, providing a clear example of curvature in algebraic functions.

Linear Function

A linear function represents a relationship with a constant rate of change and is graphically displayed as a straight line. Typically expressed as f(x) = mx + b, where m is the slope and b is the y-intercept, it is foundational for understanding proportional relationships.

Square Root Function

A square root function, expressed as f(x) = ?x, involves the extraction of the square root of the input. The graph of a square root function starts at the origin (or from a shifted locus) and gradually increases, illustrating a non-linear, but continuously increasing, output within a restricted domain of non-negative values.

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