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3 years ago

-2x + 7 < 23 which graph ?

Mathematics

1 answer:

Ilya [14]3 years ago

6 0

Answer:

The red one/bottom one. x>-8

Step-by-step explanation:

Subtract 7 giving you 16. Divide by negative 2 which gives you -8, but since your dividing by a negative you have to flip the sign. The Answer is x>-8. The Sign points which way you have to shade, the answer is which point you shade at, and the opened circle means that it is NOT equal to that answer but it is bigger. Closed circle if it is equal to. ;)

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What is the effect on the graph of the function f(x) = x^2 when f(x) is changed to f(x − 6)

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Answer:

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing $f(x) = x^2$ and $\:f\left(x\right)=\left(x-6\right)^2$ is represented as being shifted 6 units to the right as compare to the function $f(x) = x^2$ .

Step-by-step explanation:

When we Add or subtract a positive constant, let say c, to input x, it would be a horizontal shift.

For example:

Type of change Effect on y = f(x)

$y = f(x - c)$ horizontal shift: c units to right

Considering the function

$f(x) = x^2$

The graph is shown below. The first figure is representing $f(x) = x^2$ .

Now, considering the function

$\:f\left(x\right)=\left(x-6\right)^2$

According to the rule, as we have discussed above, as a positive constant 6 is added to the input, so there is a horizontal shift, 6 units to the right.

The graph of $\:f\left(x-6\right)=\left(x-6\right)^2$ is shown below in second figure. It is clear that the graph of $\:f\left(x-6\right)=\left(x-6\right)^2$ is shifted 6 units to the right as compare to the function $f(x) = x^2$ .

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3 years ago