The blue line depicted in the attached image illustrates the reflection of f(x) across the x-axis.
To elucidate, the function f(x) is an exponential function displaying the characteristics: the y-intercept calculates as f(0) = 6(0.5)⁰ = 6; the multiplicative rate of change is 0.5, signifying a decay function (decreasing); and the horizontal asymptote exists at y = 0, defining the limit of f(x) as x approaches positive infinity. The reflection across the x-axis for f(x) results in a function denoted as g(x) = -f(x), leading to g(x) reflecting the features discussed including growth into the third quadrant while never intersecting the x-axis. Therefore, using these insights, it is feasible to sketch the corresponding graph across the x-axis.
(5x - 3y)(25x² + 15xy + 9y²) Step-by-step explanation: 125x³ - 27y³ is a difference of cubes and can be factored as a³ - b³ = (a - b)(a² + ab + b²). Given 125x³ - 27y³ = (5x)³ - (3y)³, it can be written as (5x - 3y)((5x)² + (5x)(3y) + (3y)²) = (5x - 3y)(25x² + 15xy + 9y²).
In this scenario, the buying price decreases with a higher purchase quantity. However, the markup for the retail price remains steady at 80% of the buying cost. If we denote the price as x, then the retail price can be expressed as:
Retail price= x * (100%+80%)
Retail price= x * 180%=
Retail price= 1.8 x
The equation remains consistent across different ranges since the markup ratio is constant. Only the buying price varies depending on how many pairs of shoes are bought.
