Math Flashcards

Is there a function in this relation?

Answer: yes

A relation is considered a function if and only if every input (x-value) corresponds to exactly one output (y-value). If the provided relation (which is missing from the prompt but implied by the question) adheres to this rule, meaning no x-value is paired with more than one distinct y-value, then it represents a function. The "yes" answer indicates that, whatever the specific relation was, it satisfied this fundamental condition for a function.

Is there a function in this relation?

Answer: yes

For a relation to be a function, each input value (typically represented by 'x') must be associated with only one output value (typically 'y'). If the given relation (which is not explicitly shown in the prompt) ensures that no single input maps to multiple different outputs, then it correctly defines a function. The answer "yes" confirms that the relation in question meets this criterion.

What is the effect on the graph of f(x) of the transformation f(x)→f(4x)?

Answer: reduces its horizontal size

The transformation f(x)→f(4x) involves a change to the input variable, x. When the input x is multiplied by a factor greater than 1 (like 4), the graph undergoes a horizontal compression. This means the graph is squeezed towards the y-axis, effectively reducing its horizontal size by a factor of 1/4.

Is there a function in this relation?

Answer: yes

A relation is considered a function if every input value (x-value) corresponds to exactly one output value (y-value). This means that for any given x, there should not be two or more different y-values associated with it. Since the correct answer is 'yes', the unspecified relation must adhere to this rule, ensuring each input has a unique output.

Which quadrant, in standard position, contains the terminal side of a 315° angle?

Answer: Quadrant IV

In standard position, angles are measured counterclockwise from the positive x-axis. Quadrant I spans 0° to 90°, Quadrant II 90° to 180°, Quadrant III 180° to 270°, and Quadrant IV 270° to 360°. A 315° angle falls between 270° and 360°, placing its terminal side in Quadrant IV.

Which quadrant, in standard position, contains the terminal side of a 135° angle?

Answer: Quadrant II

In standard position, angles are measured counterclockwise from the positive x-axis. Quadrant I spans 0° to 90°, Quadrant II 90° to 180°, Quadrant III 180° to 270°, and Quadrant IV 270° to 360°. A 135° angle falls between 90° and 180°, placing its terminal side in Quadrant II.

Which quadrant, in standard position, corresponds to the terminal side of a 225° angle?

Answer: Quadrant III

In standard position, angles are measured counterclockwise from the positive x-axis. Quadrant I spans 0° to 90°, Quadrant II 90° to 180°, Quadrant III 180° to 270°, and Quadrant IV 270° to 360°. A 225° angle falls between 180° and 270°, placing its terminal side in Quadrant III.

Which quadrant, in standard position, contains the terminal side of a 45° angle?

Answer: Quadrant I

In standard position, angles are measured counterclockwise from the positive x-axis. Quadrant I spans 0° to 90°, Quadrant II 90° to 180°, Quadrant III 180° to 270°, and Quadrant IV 270° to 360°. A 45° angle falls between 0° and 90°, placing its terminal side in Quadrant I.

The terminal side of a 690° angle in standard position lies in which quadrant?

Answer: Quadrant IV

To find the quadrant for an angle greater than 360°, subtract multiples of 360° until you get an angle between 0° and 360°. For 690°, 690° - 360° = 330°. Since 330° lies between 270° and 360°, its terminal side is in Quadrant IV.

The terminal side of a 480° angle in standard position lies in which quadrant?

Answer: Quadrant II

To find the quadrant for an angle greater than 360°, subtract multiples of 360° until you get an angle between 0° and 360°. For 480°, 480° - 360° = 120°. Since 120° lies between 90° and 180°, its terminal side is in Quadrant II.

Which quadrant, in standard position, corresponds to the terminal side of a 150° angle?

Answer: Quadrant II

In standard position, angles are measured counterclockwise from the positive x-axis. Quadrant I spans 0° to 90°, Quadrant II 90° to 180°, Quadrant III 180° to 270°, and Quadrant IV 270° to 360°. A 150° angle falls between 90° and 180°, placing its terminal side in Quadrant II.