Unit 1 So Far

Front

Which parent function matches the graph?
Options: f(x) = a⋅b^x, f(x) = ∛(x), f(x) = √(x), f(x) = x²

Back

f(x) = ∛(x)

Answer explanation

The graph of f(x) = ∛(x) represents a cube root function, which has a characteristic shape that increases slowly and passes through the origin. This matches the given graph, while the other options do not.

Front

What is the name of this parent function?

Back

Cubic Function

Answer explanation

The parent function represented by the equation y = x^3 is known as the Cubic Function. It is characterized by its degree of 3, which distinguishes it from Linear (degree 1), Quadratic (degree 2), and Square Root functions.

Front

What is the name of this parent function? Options: Quadratic Function, Square Root Function, Exponential Function, Absolute Value Function

Back

Absolute Value Function

Answer explanation

The parent function represented by the absolute value is characterized by a V-shape graph, which is distinct from the other options. Therefore, the correct answer is the Absolute Value Function.

Front

What is the y-intercept of the graph shown? Options: (1, 0), (3, -4), (0, 5), (5, 0)

Back

(0, 5)

Answer explanation

The y-intercept is the point where the graph crosses the y-axis, which occurs when x = 0. The correct choice (0, 5) indicates that when x is 0, y is 5, confirming it as the y-intercept.

Front

Which parent function is this? Options: Quadratic, Cubic, Linear, Rational

Back

Rational

Answer explanation

The correct answer is 'Rational' because a rational function is defined as the ratio of two polynomials. This distinguishes it from quadratic, cubic, and linear functions, which have different forms and characteristics.

Front

Domain is:

Back

All x values, from left to right.

Answer explanation

The domain of a function refers to all possible x values. Therefore, the correct choice is 'All x values, from left to right,' as it accurately describes the range of x values that can be input into the function.

Front

Range is:

Back

All y values, from bottom to top.

Answer explanation

The range of a function refers to all possible output values (y values). Therefore, the correct choice is 'All y values, from bottom to top,' as it describes the vertical extent of the graph.

Front

State the DOMAIN in interval notation.

Back

(-∞,∞)

Answer explanation

The domain of a function is the set of all possible input values. The correct choice, (-∞,∞), indicates that all real numbers are included, meaning any real number can be an input.

Front

What are the asymptotes? Options: x = −3 y = 1 , x = 3 y = 1, x = −3 y = −1, x = 3 y = −1

Back

x = −3 y = 1

Answer explanation

The asymptotes of a function are the lines that the graph approaches but never touches. For this question, the correct asymptotes are x = -3 and y = 1, indicating vertical and horizontal asymptotes respectively.

Front

What is the green dot on the parabola called?

Back

maximum

Answer explanation

The green dot on the parabola represents the maximum point, where the curve reaches its highest value. In a downward-opening parabola, this point is called the maximum, distinguishing it from minimum points or roots.