A dilation is a transformation whose preimage and image are
1 answer:
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Using slope-intercept form, y = mx + b where m = slope and b = y-intercept:
We know our slope is -6. This can be interpreted as -6/1, which rise-over-run-wise, means that when y changes by 6, x changes inversely by 1.
To find that y-intercept, though, we need to find the value of y when x = 0.
Use our point (-9, -3) to find this...
We want to add 9 to x so that it becomes 0.
According to our slope, this means subtracting 54 from y.
Our y-intercept is at (0, -57), with -57 being the value of b we put in our equation.
You could also just use point-slope form:
y - y¹ = m(x - x¹)
y - (-3) = -6(x - (-9))
y + 3 = -6(x + 9)
And convert to slope-intercept if you want:
y + 3 = -6x - 54
y = -6x - 57
We know our slope is -6. This can be interpreted as -6/1, which rise-over-run-wise, means that when y changes by 6, x changes inversely by 1.
To find that y-intercept, though, we need to find the value of y when x = 0.
Use our point (-9, -3) to find this...
We want to add 9 to x so that it becomes 0.
According to our slope, this means subtracting 54 from y.
Our y-intercept is at (0, -57), with -57 being the value of b we put in our equation.
You could also just use point-slope form:
y - y¹ = m(x - x¹)
y - (-3) = -6(x - (-9))
y + 3 = -6(x + 9)
And convert to slope-intercept if you want:
y + 3 = -6x - 54
y = -6x - 57
Answer:
- doman: x ≠ 1
- range: y ≠ 7
Step-by-step explanation:
The domain is the horizontal extent of the graph, the set of x-values for which the function is defined. The range is the vertical extent of the graph, the set of y-values defined by the function.
<h3>Simplified</h3>The given function is undefined where its denominator is zero, at x=1. Everywhere else, it can be simplified to ...
The simplified function (3x+4) is defined for all values of x except x=1. The simplest description is ...
x ≠ 1
In interval notation, this is ...
(-∞, 1) ∪ (1, ∞)
<h3>Range</h3>
The simplified function is capable of producing all values of y except the one corresponding to x=1: 3(1)+4 = 7. The simplest description is ...
y ≠ 7
In interval notation, this is ...
(-∞, 7) ∪ (7, ∞)
