Question

a remote - control car moves toward a wall, stops, backs up, and stops. the graph shows the cars distance from the wall as a function of time. answers parts a through d.
a. write the domain and range in inequalities. identify the domain. select the correct choice below and fill in the answer box(es) to complete your choice.
a. ( leq y leq )
b. ( x leq )
c. ( leq x )
d. ( y leq )
e. ( leq x leq )
f. ( leq y )

Explanation:

To solve part (a) about the domain of the function (distance from the wall as a function of time), we analyze the time axis (x - axis) of the graph:

Step 1: Identify the minimum and maximum time values

From the graph, the time starts at \( t = 0 \) seconds (when the car starts moving) and ends at \( t = 10 \) seconds (when the car stops for the second time). So the domain (set of all possible \( x \) - values, where \( x \) represents time) is the set of all real numbers \( x \) such that \( 0\leq x\leq10 \).

Looking at the options:

• Option A: \( \leq y\leq \) (incorrect, as domain is about \( x \), not \( y \))
• Option B: \( x\leq \) (incomplete and incorrect, we need a range for \( x \))
• Option C: \( \leq x \) (incomplete and incorrect)
• Option D: \( y\leq \) (incorrect, domain is about \( x \))
• Option E: \( \leq x\leq \) (this is the correct form for the domain inequality, we fill in \( 0 \) and \( 10 \) to get \( 0\leq x\leq10 \))
• Option F: \( \leq y \) (incorrect, domain is about \( x \))

Answer:

E. \( 0\leq x\leq10 \) (assuming the end time from the graph is 10 seconds, we fill in the blanks in the \( \leq x\leq \) form with the minimum and maximum time values from the graph)