Question

the equation $y = x^2 + 1$ represents a function. use the function rule to complete the table. input ($x$) output ($y$) -2 5 -1 0 ? 1 ? 2 ?

Explanation:

Step1: For \( x = -1 \)

Substitute \( x = -1 \) into \( y = x^2 + 1 \). Calculate \( (-1)^2 = 1 \), then \( y = 1 + 1 = 2 \).

Step2: For \( x = 0 \)

Substitute \( x = 0 \) into \( y = x^2 + 1 \). Calculate \( 0^2 = 0 \), then \( y = 0 + 1 = 1 \).

Step3: For \( x = 1 \)

Substitute \( x = 1 \) into \( y = x^2 + 1 \). Calculate \( 1^2 = 1 \), then \( y = 1 + 1 = 2 \).

Step4: For \( x = 2 \)

Substitute \( x = 2 \) into \( y = x^2 + 1 \). Calculate \( 2^2 = 4 \), then \( y = 4 + 1 = 5 \).

Answer:

For \( x = -1 \), \( y = 2 \); for \( x = 0 \), \( y = 1 \); for \( x = 1 \), \( y = 2 \); for \( x = 2 \), \( y = 5 \). So the completed table (row - by - row for the empty cells) has outputs 2, 1, 2, 5.