Graphing Square Root Functions

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Exercises 6 The domain of radical functions only includes values for which the radicand is greater than or equal to 0. y=4x​​ We can solve for these values of x by only looking at the radicand. 4x≥0⇔x≥0​ The domain is all real numbers greater than or equal to 0.
Exercises 7 The domain of radical functions only includes values for which the radicand is greater than or equal to 0. y=4+-x​​ We can solve for these values of x by only looking at the radicand. -x≥0⇔x≤0​ The domain is all real numbers less than or equal to 0.
Exercises 8 The domain of radical functions only includes values for which the radicand is greater than or equal to 0. y=-21​x​+1​ We can solve for these values of x by only looking at the radicand. -21​x≥0⇔x≤0​ The domain is all real numbers less than or equal to 0.
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Exercises 10 The domain of radical functions only includes values for which the radicand is greater than or equal to 0. p(x)=x+7​​ We can solve for these values of x by only looking at the radicand. x+7≥0⇔x≥-7​ The domain is all real numbers greater than or equal to -7.
Exercises 11 The domain of radical functions only includes values for which the radicand is greater than or equal to 0. f(x)=-x+8​​ We can solve for these values of x by only looking at the radicand. -x+8≥0LHS−8≥RHS−8-x≥-8Multiply by -1 and flip inequality signx≤8 The domain is all real numbers less than or equal to 8.
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Exercises 15 In order to identify the graph of the given function, we will first find the function's domain. After matching the graph, we will be able to describe the range.Domain The domain of radical functions only includes values for which the radicand is greater than or equal to 0. y=x−3​​ We can solve for these values of x by only looking at the radicand. x−3≥0⇔x≥3​ The domain is all real numbers greater than or equal to 3.Graph and Range Next, we will draw the graph of the function and match it to one of the given options. To graph the function, we will make a table of values. Remember to use values for x that are included in the domain.xx−3​y=x−3​ 33−3​0 44−3​1 55−3​≈1.41 66−3​≈1.73 77−3​2 Let's now plot the points and connect them with a smooth curve.This graph corresponds to option D. We can see that the range is all real numbers greater than or equal to 0. Range: y≥0​
Exercises 16 In order to identify the graph of the given function, we will first find the function's domain. After matching the graph, we will be able to describe the range.Domain The domain of radical functions only includes values for which the radicand is greater than or equal to 0. y=3x​​ We can solve for these values of x by only looking at the radicand. x≥0​ The domain is all real numbers greater than or equal to 0.Graph and Range Next, we will draw the graph of the function and match it to one of the given options. To graph the function, we will make a table of values. Remember to use values for x that are included in the domain.x3x​y=3x​ 030​0 131​3 232​≈4.24 333​≈5.2 434​6 Let's now plot the points and connect them with a smooth curve.This graph corresponds to option C. We can see that the range is all real numbers greater than or equal to 0. Range: y≥0​
Exercises 17 In order to identify the graph of the given function, we will first find the function's domain. After matching the graph, we will be able to describe the range.Domain The domain of radical functions only includes values for which the radicand is greater than or equal to 0. y=x​−3​ We can solve for these values of x by only looking at the radicand. x≥0​ The domain is all real numbers greater than or equal to 0.Graph and Range Next, we will draw the graph of the function and match it to one of the given options. To graph the function, we will make a table of values. Remember to use values for x that are included in the domain.xx​−3y=x​−3 00​−3-3 11​−3-2 22​−3≈-1.59 33​−3≈-1.27 44​−3-1 Let's now plot the points and connect them with a smooth curve.This graph corresponds to option A. We can see that the range is all real numbers greater than or equal to -3. Range: y≥-3​
Exercises 18 In order to identify the graph of the given function, we will first find the function's domain. After matching the graph, we will be able to describe the range.Domain The domain of radical functions only includes values for which the radicand is greater than or equal to 0. y=-x+3​​ We can solve for these values of x by only looking at the radicand. -x+3≥0LHS−3≥RHS−3-x≥-3Multiply by -1 and flip inequality signx≤3 The domain is all real numbers less than or equal to 3.Graph and Range Next, we will draw the graph of the function and match it to one of the given options. To graph the function, we will make a table of values. Remember to use values for x that are included in the domain.x-x+3​y=-x+3​ 3-3+3​0 2-2+3​1 1-1+3​≈1.41 0-0+3​≈1.73 -1-(-1)+3​2 Let's now plot the points and connect them with a smooth curve.This graph corresponds to option B. We can see that the range is all real numbers greater than or equal to 0. Range: y≥0​
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