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(i) To find $f(\\var{x1})$, you start at $\\var{x1}$ on the $x$-axis, go up or down until you reach the blue line, and then look at the $y$-coordinate. This $y$-coordinate is the answer.  In this question, after going up/down from $\\var{x1}$, we reach the $y$-coordinate $\\var{y1}$, so the answer is $f(\\var{x1})=\\var{y1}$.

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(ii) There are two options. The first option (which is not efficient) is trial-and-error: pick some random value of $x$ and determine $f(x)$. If $f(x) = \\var{y2}$, then your pick is the answer.  If not, then try a different value of $x$, hopefully getting closer and closer each time.   The second (and better) option is to 'work backwards' - we know what $f(x)$ should be, which means we know what the $y$-coordinate should be.  So start at $\\var{y2}$ on the $y$-axis, go left or right until you reach the blue line, and look at the $x$-coordinate. In this question, after going left/right from $\\var{y2}$, we reach the $x$-coordinate $\\var{x2}$, so this is the answer.  You can check this is correct: what is $f(\\var{x2})$? It is $\\var{y2}$, as we wanted!

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(iii) This question is asking exactly the same thing as the question in (ii), but is phrased differently. This is because the definition of $f^{-1}$ is that it is the function which un-does what $f$ does.  For example, we know that $f(\\var{x1})=\\var{y1}$ - therefore, automatically, $f^{-1}(\\var{y1})$ has to be $\\var{x1}$.  Re-worded, $f$ maps $\\var{x1}$ to $\\var{y1}$, so because $f^{-1}$ un-does this, it means $f^{-1}$ maps $\\var{y1}$ back to $\\var{x1}$.   Back to the question at hand, it asked what $f^{-1}(\\var{y2})$ is.  By definition, this means we want to know what value of $x$ is needed to get $f(x) = \\var{y2}$, which is exactly what was asked in (ii). 

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Reading a graph.

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{eqnline(a, hshift, vshift)}

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Above is the graph of some function $f$.

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What is $f(\\var{x1})$? [[0]]

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What value of $x$ do you need to get $f(x) = \\var{y2}$? [[1]]

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What is $f^{-1}(\\var{y2})$? [[2]]

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A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

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Random amount of vertifical shift for sake of variability.

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Coefficient of x^3

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Random amount of horizontal shift to create variability.

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