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Chapter 4: Problem 3

a) Evaluate \(y=5 x-8\) for \(x=3\) b) If \(f(x)=5 x-8,\) find \(f(3)\)

Short Answer

Expert verified
a) \(y=7\) b) \(f(3)=7\)

Step by step solution

01

Evaluate the function at \(x=3\)

To evaluate the function \(y=5x-8\) at \(x=3\), we substitute the value of x into the equation: \(y = 5(3) - 8\) Now, simply calculate the value of y: \(y = 15 - 8\) \(y = 7\) So, the value of y when \(x=3\) is 7.
02

Use the function notation to find \(f(3)\)

To find the value of the function \(f(x)=5x-8\) when \(x=3\), we substitute the value of x into the function: \(f(3) = 5(3) - 8\) Now, simply calculate the value of f(3): \(f(3) = 15 - 8\) \(f(3) = 7\) So, the value of the function \(f(x)\) when \(x=3\) is \(f(3)=7\). In conclusion, both parts (a) and (b) give the same result: when \(x=3\), \(y=7\) and \(f(3)=7\). This is because the equation \(y=5x-8\) and the function \(f(x)=5x-8\) represent the same relationship between x and y.

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Most popular questions from this chapter

Lines \(L_{1}\) and \(L_{2}\) contain the given points. Determine if lines \(L_{1}\) and \(L_{2}\) are parallel, perpendicular, or neither. $$\begin{aligned}&L_{1}:(-1,-7),(2,8)\\\&L_{2}:(10,2),(0,4)\end{aligned}$$

Write an equation of the line parallel to the given line and containing the given point. Write the answer in slope intercept form or in standard form, as indicated. $$y=2 x+1 ;(-2,-7) ; \text { standard form }$$

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Write an equation of the line parallel to the given line and containing the given point. Write the answer in slope intercept form or in standard form, as indicated. $$y=\frac{1}{2} x-5 ;(4,5) ; \text { standard form }$$
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