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Functions: Domain and Range

Functions: Domain and Range. Review: Find the domain and range of the function:. Domain: {list all x values in table } in numeric order without listing repeats Range: {list all y values in table } in numeric order without listing repeats. This is the same as Domain: {0, -9, 3, 4, -12}

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Functions: Domain and Range

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  1. Functions:Domain and Range

  2. Review:Find the domain and range of the function: Domain: {list all x values in table} in numeric order without listing repeats Range: {list all y values in table} in numeric order without listing repeats This is the same as Domain: {0, -9, 3, 4, -12} Range: {10, 8, 10, -5, -15} you might see it written this way sometimes but numeric order is better Domain: {-12, -9, 0, 3, 4} Range: {-15, -5,8,10} Domain: {3, 5, 6, 10, 12} Range: {-15, -12, -4,-2, 5}

  3. Find the domain of the function: • f(x) = 3x + 9 • If there aren’t exact values to list, describe the domain • The domain (x values) could be any real number. • D = {all real numbers} • f(x) = • You can’t take the square root of a negative number, but 0 and larger is ok • The domain is any real number ≥ 5. • D = {All real numbers ≥ 5 } or could write it as D = {x >5} • f(x) = • The denominator cannot equal zero. • The domain is any real number except 4. • D = {All real numbers 4} *Tip – to find the number it can’t be or what it should be greater or less than, set the expression inside = 0 or denominator = 0 and solve x - 4 = 0 x = 4 , so x can’t be 4

  4. Find the domain of the relation: Domain: {-2 < x < 2} Domain: {all real numbers} • Even though you can’t see all x values of this function from the graph, it will go on forever in each direction (we will learn more about identifying that later) • This is NOT a function, but the relation still has a domain and range Domain: {x > 0} Domain: {all integers} • Notice this ends up being a discrete graph

  5. Find the domain and range of the function: • The temperature in a house drops 2°F for every hour the air conditioner is on between the hours 6:00 am and 11:00 am. The following is a list of times and temperatures in the house: 6 am, 82°F; 8 am 78°F; 9 am 76°F; 10 am, 74°F, and 11 am, 72°F. • Domain: {6, 8, 9, 10, 11} • Range:{72, 74, 76, 78, 82}

  6. Find the domain of the function: • If the function f(n) represents the number of hours required to construct n pizzas at dinner time at the local delivery joint, what domain makes sense? • You can’t make negative pizzas or partial pizzas. • Domain: {whole numbers ≥ 0} • Will the graph of this be discrete or continuous? • Discrete!

  7. Find the domain of the function: • Your cell phone plan charges you $0.20 for each text message you send. Your parents put a cap of $50 on your texting bill each month. If f(x) = 0.2x is the cost of the total number of texts you send per month, what is the domain of the function? • First find the maximum amount of texts you can send each month by substituting 50 in where f(x) is. • 50 = 0.2x • x = 250 • You cannot go over 250 texts. • Can you have negative text messages? • Write the domain. • Domain:{0 ≤ x ≤ 250} So the largest amount you can have is 250 No, so the smallest amount you can have is 0

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