Exercises: Linear functions, zeros, axis intercepts

Consider the linear function $f (x) = 3 - \frac{12}{7} x$ .

Draw the graph and mark the function value $f (- 1)$ .

Draw the graph and mark the function value $f (- 1)$ .
Is the point $P (\sqrt{7} | - 1,54)$ on the graph of $f (x)$ ?

Check whether the point $P (\sqrt{7} | - 1.54)$ lies on the graph of the function.
To do this, insert the $x$ -value $\sqrt{7}$ into the function equation $y (x) = 3 - \frac{12}{7} x$ .
$3 - \frac{12}{7} \cdot \sqrt{7}$ $\approx$ $3 - \frac{12}{7} \cdot 2.65$
↓
multiply
$\approx$ $3 - 4.543$
↓
subtract
$\approx$ $- 1.543$
Result
The point $P (\sqrt{7} | - 1.54)$ is not on the graph because the function value of $\sqrt{7}$ is a non-terminating decimal fraction and not the finite decimal fraction $- 1.54$ .
If you have calculated with rounded values, you might have mistakenly conclude that the point is on the graph. However, this is not the case.

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