How do I graph f ≥ 2 on x ∈ (-∞, -4)?

Asked Oct 16 '22 at 14:30

Active Oct 16 '22 at 14:55

Viewed 39 times

I'm a little thrown off by how this function is written.

But how do I approach sketching the function in the cartesian plane?

$f ≥ 2$ on $x ∈ (-∞, -4)$

Do I just draw a line $x ≥ 2$ on between but not exclusively $ (-∞, -4)$?

$x$ is in the set of $(-∞, -4)$, so does this mean I draw a point on y-axis $2,0$, and it does upwards but doesn't touch $x=-4$?

I think what's throwing me off is questions usually are like $f(x) = x^2 + 2$ if $x ≥ 0$

is $f ≥ 2$ referring to the y or x-axis?

Someone got a guide on graphing piecewise functions?

EDIT: the question says "sketch the possible function".

edited Oct 16 '22 at 14:55

asked Oct 16 '22 at 14:30

Strider

$f(x)$ is the value of the function, so you want $y = f(x) \geq 2$ for each $x \in (-\infty, -4)$. – N. F. Taussig Oct 16 '22 at 15:00
so is that like a line pointing top left at y = 2 from x = -4 to -∞ ? – Strider Oct 16 '22 at 15:23
sorry - can you sketch a possible solution so i can visualise it? – Strider Oct 16 '22 at 15:23
The function $f(x) = 2$ is one example, as is the function defined by $f(x) = -x$. In both cases, $f(x) \geq 2$ everywhere in the interval $(-\infty, -4)$. This question has multiple possible answers. Just pick one and draw a sketch of its graph. – N. F. Taussig Oct 16 '22 at 15:52
ok - what's the difference between $f$ and $f(x)$? – Strider Oct 16 '22 at 15:59
if f(x) = -x, the line would be slopping down from -infinity to x=-4 correct? – Strider Oct 16 '22 at 16:04
$f$ is the function; $f(x)$ is the value of the function at $x$. This distinction is not always made clear. See, for instance, What is the difference between writing $f$ and $f(x)$?. – N. F. Taussig Oct 16 '22 at 16:05
In answer to your latest comment, yes. – N. F. Taussig Oct 16 '22 at 16:05

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