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Chapter 1: Problem 35

(a) use a graphing utility to graph the function and find the zeros of the function and (b) verify your results from part (a) algebraically. $$ f(x)=\sqrt{2 x+11} $$

Short Answer

Expert verified
The zeros or roots of the function are verified by both graphing and algebraic methods. If we set \(f(x) = 0\) and solve for 'x', we get the algebraic solution. Checking the graph, output at these 'x' values will be zero, therefore confirming that these 'x' values are indeed the roots of the function.

Step by step solution

01

Graph the Function

Use a graphing utility to graph the function \(f(x) = \sqrt{2x + 11}\). Start by plotting the function for various x-values and outline the resulting graph. Notice the range of this function will be \([0, \infty)\) because the square root function only returns non-negative numbers.
02

Identify the zeros of the Function

The zeros of the function are x-values that make \(f(x) = 0\). On your graph, these are the points where f(x) intersects the x-axis. Identify those points on your graph.
03

Verify the zeros algebraically

The zero(s) or root(s) of the function is/are real number(s) that make the function equal to zero. Set \(f(x) = 0\) in the equation, solve for x by squaring both sides. Those values of x are your zeros.
04

Compare the Results

Compare the x-values from the graph with those found by solving \(f(x)=0\). They should match, verifying your graphing results algebraically

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Most popular questions from this chapter

Prove that if \(f\) and \(g\) are one-to-one functions, then \((f \circ g)^{-1}(x)=\left(g^{-1} \circ f^{-1}\right)(x) .\)

Find a mathematical model for the verbal statement. \(F\) varies directly as \(g\) and inverselv as \(r^{2}\).

(a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=\frac{4}{x} $$

The linear model with the least sum of square differences is called the _____ _____ _____ line.

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