Debbie is a runner, and the map below shows the route she runs each day. The distance from her house to Bearcat Street is 4x2−8x−1 miles, and the distance from Lois’ Tea Emporium to St. Teresa’s Cathedral is double this distance. If the distance from Bearcat Street to Lois’ Tea Emporium is six more than the distance from Debbie’s house to Bearcat Street and the distance from St. Teresa’s Cathedral to Debbie’s house is five less than the distance from Lois’ Tea Emporium to St. Teresa’s Cathedral, find an expression that represents the total number of miles Debbie runs each day.

she will travel a distance in the range of 3 - 11 miles

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation:

p

step-by-step explanation: