Hich function has a range of {y|y ≤ 5}? f(x) = (x – 4)2 + 5 f(x) = –(x – 4)2 + 5 f(x) = (x – 5)2 + 4 f(x) = –(x – 5)2 + 4

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

where

(h,k) is the vertex of the parabola

if a>0 -----> the parabola open upward (vertex is a minimum)

if a<0 -----> the parabola open downward (vertex is a maximum)

Verify each case

case A)

The vertex is the point

a>0 -----> the parabola open upward (vertex is a minimum)

The range is the interval--------> [5,∞)

case B)

The vertex is the point

a<0 -----> the parabola open downward (vertex is a maximum)

The range is the interval--------> (-∞,5]

case C)

The vertex is the point

a>0 -----> the parabola open upward (vertex is a minimum)

The range is the interval--------> [4,∞)

case D)

The vertex is the point

a<0 -----> the parabola open downward (vertex is a maximum)

The range is the interval--------> (-∞,4]

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

first one because it can't have a fraction in it

step-by-step explanation: