Question

PLS ACTUALLY HELP IT'S DUE TN

Answer 1

Average rate of change = -4

Explanation:

Given:

f(x) = x² + 7x + 10

-8 ≤ x ≤ -3 or [-8, -3] in interval notation

Average rate of change of the function can be solved using the formula:

`\mathrm{Average\:rate\:of\:change} = ( f \left( b \right) -f \left( a \right) )/( b-a )`

`\mathrm{Average\:rate\:of\:change} = ( f \left( -3 \right) -f \left( -8 \right) )/( -3 - (-8) )`

`\mathrm{Average\:rate\:of\:change} = ( f \left( -3 \right) -f \left( -8 \right) )/( -3 + 8 )`

`\mathrm{Average\:rate\:of\:change} = ( f \left( -3 \right) -f \left( -8 \right) )/( 5 )`

Substitute x = -3 to the given function for f(-3) and x = -8 for f(-8)

`\mathrm{Average\:rate\:of\:change} = ( f \left( -3 \right) -f \left( -8 \right) )/( 5 )`
`\mathrm{Average\:rate\:of\:change} = \frac{ { \left[( -3 \right) }^( 2 ) +7 \left( -3 \right) +10]- { \left[( -8 \right) }^( 2 ) +7 \left( -8 \right) +10] }{ 5 }`

`\mathrm{Average\:rate\:of\:change} = ( [9-21+10]-[64-56+10] )/( 5 )`

`\mathrm{Average\:rate\:of\:change} = ( [-2]-[18] )/( 5 )`

`\mathrm{Average\:rate\:of\:change} = ( - 20 )/( 5 )`

`\mathrm{Average\:rate\:of\:change} = {-4 }`