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Question Video: Recognizing the Relationship between the Input and Output of a Function Mathematics • 9th Grade

Given the function 𝑓, the meaning of 𝑓(π‘Ž βˆ’ 1) is β€œthe output when the input is 1 less than π‘Žβ€. Interpret the following. 1) 𝑓(𝑏 + 3). 2) 𝑓(𝑠) βˆ’ 3. 3) 𝑓(3 βˆ’ π‘₯). 4) 𝑓(𝑏) βˆ’ 𝑓(π‘Ž). 5) 𝑓(3𝑑). 6) 𝑓(π‘Ž)^𝑏.

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Video Transcript

Given the function 𝑓, the meaning of 𝑓 of π‘Ž minus one is the output when the input is one less than π‘Ž. Interpret the following. 𝑓 of 𝑏 plus three, 𝑓 of 𝑠 minus three, 𝑓 of three minus π‘₯, 𝑓 of 𝑏 minus 𝑓 of π‘Ž, 𝑓 of three 𝑑, and 𝑓 of π‘Ž to the power 𝑏.

Before starting this question, it is worth recalling what we mean by a function 𝑓. If we have any function 𝑓 of π‘₯, then π‘₯ is the input and 𝑓 of π‘₯ is the output. A number inside the bracket affects the input, whereas a number outside of the bracket affects the output. This can be seen from the example, as π‘Ž minus one means one less than π‘Ž.

Our first function, 𝑓 of 𝑏 plus three, is very similar to the example. Instead of subtracting one from π‘Ž, we’re adding three to 𝑏. This means that 𝑓 of 𝑏 plus three calculates the output when the input is three more than 𝑏.

Our second function, 𝑓 of 𝑠 minus three, is slightly different. This time, the three that is being subtracted is outside of the bracket. 𝑓 of 𝑠 will be the output when the input is 𝑠. Therefore, 𝑓 of 𝑠 minus three is three less than the output when the input is 𝑠.

Our third function, 𝑓 of three minus π‘₯, is very similar to the first one and also the example. This time, our function gives us the output when the input is π‘₯ less than three. We are subtracting π‘₯ from three and then working out the output.

Our fourth function has two variables, 𝑏 and π‘Ž. We have 𝑓 of 𝑏 minus 𝑓 of π‘Ž. This means that we are subtracting the value of 𝑓 of π‘Ž from the value of 𝑓 of 𝑏. This is the difference between them. Therefore, the answer corresponds to the change in output when the input changes from π‘Ž to 𝑏.

The penultimate function is 𝑓 of three 𝑑. We are multiplying our value of 𝑑 by three. This is a similar idea once again to our first function, 𝑓 of 𝑏 plus three, and also our third function, 𝑓 of three minus π‘₯. This time, it corresponds to the output when the input is three times 𝑑.

Our final function involves exponents or powers. We have 𝑓 of π‘Ž to the power of 𝑏. As the 𝑏 is outside of the bracket or parentheses, this is the result of raising the output at input π‘Ž to the 𝑏th power. If the power 𝑏 was inside the bracket, we would be raising the input to the 𝑏th power. Interpreting and often drawing functions of this type is an important part of the topic.

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