Question

1. use the description and graph to compare the two functions. which function has the lesser minimum?

g(x) f(x)
nonlinear
increasing when x>3
x - intercepts at (-3,0) and (9,0)
minimum at (3,-6)
end behavior: as x→ -∞, f(x)→∞, and as x→∞, f(x)→∞
a f(x) b g(x) has a lesser minimum.

1. use these key features to sketch the graph of f(x):

● linear
● increasing for no values of x
● y - intercept located at (0,3)
● x - intercept located at (2,0)
● end behavior: as x→∞, y→ -∞

1. graph 3x - 4y = 16 by using the x - and y - intercepts.
2. graph y + 2 < 4x + 1

Explanation:

Step1: Identify the minimum of \(g(x)\)

From the graph of \(g(x)\), the minimum value of \(g(x)\) is \(y = 0\) (the lowest - point on the graph of \(g(x)\) is at the vertex which lies on the \(x\) - axis).

Step2: Identify the minimum of \(f(x)\)

Given that the minimum of \(f(x)\) is at the point \((3,-6)\), so the minimum value of \(f(x)\) is \(y=-6\).

Step3: Compare the minimum values

Compare \(-6\) and \(0\). Since \(-6<0\), \(f(x)\) has the lesser minimum.

Answer:

A. \(f(x)\)