Question

many people consider mathematician ada lovelace to be the world’s first computer programmer. lovelace used functions to write programs for an early computing machine. certain inputs (such as pressing a certain key on a keyboard) caused certain outputs. here’s a table that shows how pressing different keys causes different movements in a video game character. could this table represent a function? explain your thinking. key pressed movement right arrow walk right left arrow walk left up arrow walk right down arrow jump

Explanation:

To determine if the table represents a function, we use the definition of a function: a relation where each input (key pressed) has exactly one output (movement). Let's check each input:

• "Right arrow" has output "Walk right" (one output).
• "Left arrow" has output "Walk left" (one output).
• "Up arrow" has output "Walk right" (one output, even if the movement name repeats, the input - output relation is still single - valued for each input).
• "Down arrow" has output "Jump" (one output).

Since every input (key pressed) is associated with exactly one output (movement), the table satisfies the definition of a function.

Answer:

Yes, this table can represent a function. Because in a function, each input (key pressed) must have exactly one output (movement). For each key pressed (Right arrow, Left arrow, Up arrow, Down arrow), there is only one corresponding movement. So, the relation between the key pressed and the movement meets the definition of a function.