Identify Parent Functions And Their Graphs

Explanation
The parent function for the family of functions is the Absolute Value Function, also known as the Absolute Value. This function is represented by |x| and it gives the distance of a number from zero on the number line. The absolute value function is defined as follows: for any real number x, if x is positive or zero, the absolute value of x is x itself, and if x is negative, the absolute value of x is -x.

Explanation
The given answer is correct because the parent function mentioned is a linear function. A linear function is a function that can be represented by a straight line on a graph. It has the form y = mx + b, where m is the slope of the line and b is the y-intercept. The term "linear" in the answer refers to this characteristic of the parent function. Therefore, the correct answer is "Linear Function, Linear."

Explanation
The graph shape described in the question is that of an absolute value function. The absolute value function is a family of functions that have a characteristic V-shape. The graph is symmetric with respect to the y-axis and the vertex is located at the origin (0,0). The absolute value function represents the distance of a number from zero, disregarding its sign.

Explanation
The parent function for the given family of functions is the square root function. This function takes the square root of the input value. The family of functions includes all the transformations and variations of the square root function, such as shifting it horizontally or vertically, stretching or compressing it, or reflecting it across the x-axis. The answer correctly identifies the parent function of the given family.

Explanation
The correct answer is "Exponential Function, Exponential." The parent function of the exponential function is the function that represents the basic form of the exponential function. In this case, the parent function is the exponential function itself, which is represented by the equation y = a^x, where a is a constant. The exponential function is characterized by the fact that the variable x is in the exponent, and it grows or decays exponentially as x increases or decreases.

Explanation
The graph shape described in the question is characteristic of exponential functions. Exponential functions have a distinct curve that starts off slowly, then rapidly increases (for positive exponential functions) or decreases (for negative exponential functions). This shape is determined by the base of the exponential function, which is a constant raised to the power of the input variable. The graph of an exponential function can be represented by the equation y = a * b^x, where a is a constant and b is the base. Therefore, the correct answer is Exponential Function, Exponential, Exponent.

Explanation
The graph shape shown in the question is that of a square root function. The square root function is a specific type of radical function where the output is the square root of the input. It has a characteristic curve that starts at the origin and gradually increases, forming a concave shape. The graph resembles the shape of a square root symbol (√) and is commonly seen in various mathematical and scientific applications.

Explanation
The graph shape described in the question is that of a rational function. A rational function is a function that can be expressed as the quotient of two polynomial functions, where the denominator is not equal to zero. The graph of a rational function typically consists of a curve with one or more vertical or horizontal asymptotes, and may have holes or breaks in the graph. Therefore, the correct answer is "Rational Function, Rational".

Explanation
The graph shape shown in the question is characteristic of a logarithmic function. Logarithmic functions have a specific curve that starts off steep and gradually flattens out as x increases. The graph is typically concave down and approaches the x-axis but never touches it. Therefore, the correct answer is "Logarithmic, Logarithmic Function, Log".

Explanation
The correct answer is "Logarithmic Function, Logs, Log Functions, Logarithmic". This answer is correct because all the terms mentioned refer to the same family of functions, which are logarithmic functions. Logarithmic functions involve the use of logarithms, which are mathematical operations that represent the inverse of exponentiation. These functions are commonly used in various fields of mathematics, science, and engineering to model exponential growth or decay, solve equations involving exponential relationships, and analyze data.

Explanation
The graph shape of a power function is characterized by a curve that can either be concave up or concave down. It can have a variety of shapes depending on the value of the power. If the power is positive, the graph will start from the bottom left and increase towards the top right. If the power is negative, the graph will start from the top left and decrease towards the bottom right. The steepness of the curve also depends on the value of the power. Overall, the graph shape of a power function exhibits exponential growth or decay.