Question

1. here are graphs that represent two functions, f and g. a. decide which function value is greater for each given input. be prepared to explain your reasoning. a. f(2) or g(2) b. f(4) or g(4) c. f(6) or g(6) d. f(8) or g(8) b. is there a value of x at which the equation f(x) = g(x) is true? explain your reasoning. c. identify at least two values of x at which the inequality f(x) < g(x) is true. d. is there a value of x at which the equation f(x) = g(x) is true? explain your reasoning. e. identify at least two values of x at which the inequality f(x) < g(x) is true.

Explanation:

Part a (sub - parts a - d)

a. \(f(2)\) or \(g(2)\)

Step1: Locate \(x = 2\) on the x - axis.

Find the corresponding \(y\) - values (function values) for \(f\) and \(g\) at \(x = 2\) by looking at the graphs.

Step2: Compare the \(y\) - values.

From the graph, at \(x = 2\), the \(y\) - value of \(g\) (the \(y\) - coordinate of the point on the line \(g\)) is greater than the \(y\) - value of \(f\) (the \(y\) - coordinate of the point on the parabola - like curve \(f\)). So \(g(2)>f(2)\).

b. \(f(4)\) or \(g(4)\)

Step1: Locate \(x = 4\) on the x - axis.

Find the \(y\) - values of \(f\) and \(g\) at \(x = 4\) from the graphs.

Step2: Compare the \(y\) - values.

At \(x = 4\), the \(y\) - value of \(f\) (from the curve \(f\)) is greater than the \(y\) - value of \(g\) (from the line \(g\)). So \(f(4)>g(4)\).

c. \(f(6)\) or \(g(6)\)

Step1: Locate \(x = 6\) on the x - axis.

Find the \(y\) - values of \(f\) and \(g\) at \(x = 6\) from the graphs.

Step2: Compare the \(y\) - values.

At \(x = 6\), the \(y\) - value of \(f\) (the peak of the curve \(f\)) is greater than the \(y\) - value of \(g\) (from the line \(g\)). So \(f(6)>g(6)\).

d. \(f(8)\) or \(g(8)\)

Answer:

\(g(2)\)