Answer:
Step-by-step explanation:
Answer:
(-3,3)
Step-by-step explanation:
Using elimination:
Multiply the first equation by 8 and the second by 5 which equals
40x+56y=48
-40-60y=-60
Now you add them together
40x+(-40x)=0 so that crosses out
56y+(-60y)= -4y
48+(-60)=-12
You now have -4y=-12
Divide by -4
y=3
Now plug in y to any of the equations
5x+7(3)=6
5x+21=6
Subtract 21 from both sides
5x=-15
Divide by 5
x=-3
Your final solution is (-3,3)
Answer: left a units, down b units
Step-by-step explanation:
<h3>Answers:</h3>
- (a) It is <u>never</u> one-to-one
- (b) It is <u>never</u> onto
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Explanation:
The graph of any constant function is a horizontal flat line. The output is the same regardless of whatever input you select. Recall that a one-to-one function must pass the horizontal line test. Horizontal lines themselves fail this test. So this is sufficient to show we don't have a one-to-one function here.
Put another way: Let f(x) be a constant function. Let's say its output is 5. So f(x) = 5 no matter what you pick for x. We can then show that f(a) = f(b) = 5 where a,b are different values. This criteria is enough to show that f(x) is not one-to-one. A one-to-one function must have f(a) = f(b) lead directly to a = b. We cannot have a,b as different values.
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The term "onto" in math, specifically when it concerns functions, refers to the idea of the entire range being accessible. If the range is the set of all real numbers, then we consider the function be onto. There's a bit more nuance, but this is the general idea.
With constant functions, we can only reach one output value (in that example above, it was the output 5). We fall very short of the goal of reaching all real numbers in the range. Therefore, this constant function and any constant function can never be onto.
