Problem 113
Question
What is the graph of a function?
Step-by-Step Solution
Verified Answer
The graph of a function represents all the ordered pairs that comprise a function. It is drawn by plotting all pairs (x, y) satisfying the function equation on a cartesian grid and then joining these points to form a curve or line.
1Step 1: Definition
A function is a relationship between two sets of numbers (usually called the domain and the range) that assigns to each member of the domain exactly one member of the range. The graph of a function f is the set of points in the plane whose coordinates (x, y) satisfy the equation y=f(x). This means each x-value is paired with exactly one y-value.
2Step 2: Graphing a Function
To graph a function, start by choosing a number for x, then calculate the corresponding value of y using the provided function. Repeat this process for various x-values and then plot these points (x, y) on a cartesian grid.
3Step 3: Visual Representation of the Function
After plotting all the points, they can be joined to form a continuous curve or line. The resulting graph represents all possible pairs of (x, y) that satisfy the function equation.
Other exercises in this chapter
Problem 112
Does \(f(x)\) mean \(f\) times \(x\) when referring to a function \(f ?\) If not, what does \(f(x)\) mean? Provide an example with your explanation.
View solution Problem 112
Begin by graphing the cube root function, \(f(x)=\sqrt[3]{x} .\) Then use transformations of this graph to graph the given function. $$h(x)=\frac{1}{2} \sqrt[3]
View solution Problem 113
Find the coefficients that must be placed in each shaded area so that the function's graph will be a line satisfying the specified conditions. ___ \(x+\) ___ \(
View solution Problem 113
Begin by graphing the cube root function, \(f(x)=\sqrt[3]{x} .\) Then use transformations of this graph to graph the given function. $$r(x)=\frac{1}{2} \sqrt[3]
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