Q. 15 - Precalculus Enhanced with Graphing Utilities

Question

For the graph of the function f,

(a) Find the domain and the range of f.

(b) Find the intercepts.

(c) Is the graph of f symmetric with respect to the x-axis, the

y-axis, or the origin?

(d) Find f (2).

(e) For what value(s) of x is f(x) = 3?

(f) Solve f(x) < 0.

(g) Graph y = f(x) + 2.

(h) Graph y = f(-x).

(i) Graph y = 2f(x).

(j) Is f even, odd, or neither?

(k) Find the interval(s) on which f is increasing.

Step-by-Step Solution

Answer

\(f(2) = 1\)

Step 1: Identify the Given Information

We are given the graph of a function \(f\) and asked to find various properties including domain, range, intercepts, symmetry, function values, and transformations.

Step 2: Answer Part (d)

From the graph, \(f(2) = 1\) (reading the y-value at \(x = 2\)).

Step 3: Note on Remaining Parts

Parts (a) through (i) require reading specific features from the provided graph. The domain and range are read from the horizontal and vertical extent of the graph. Intercepts are where the graph crosses the axes. Symmetry is tested by checking if \(f(-x) = f(x)\), \(f(-x) = -f(x)\), or neither.