Question

Help please! I dont understand this, and ive been trying for a while now but i cant figure it out

Answer 1

OK, f is the graph and g is the table.

f(-2) > g(-2)

f(-2) means the y coordinate of the graph when x=-2.  That's y=2, so f(-2)=2

g(-2) we look up in the table, g(-2)=1

So it's true that f(-2) > g(-2)

Answer: f(-2) > g(-2)   TRUE

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The characteristic of an absolute value function, possibly shifted and scaled, is the distinct V shape.   Clearly f is an absolute value function; the slopes are -1 and 1 and the vertex is at (-3,1) so f(x) = |x+3|+1

g kinda also has the characteristic V shape, but it has a slope of -3  in one place and -1 in the other, so it isn't a straight line.

Answer: f(x) and g(x) are absolute value functions.   FALSE

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For all x, f(x) > g(x)

Presumably this means for all x in g's domain, which is only five points.  We already checked x=-2; let's do the rest.

f(-5) = 3, g(-5) = 4

So at x=-5 it's not true

For all x, f(x) > g(x)   FALSE

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f(x) and g(x) intersect at exactly two points.

We already know they don't at x=-5 and x=-2.  Let's check the other three.

f(-5) = 3, g(-5) = 4

f(-4) = 2,  g(-4)=1

f(-3) = 1, g(-3) = 0

f(-2) = 2, g(-2) = 1

f(-1) = 3, g(-1) = 4

This one's tricky.   All we really know about g is the points listed.   g may be a parabola where the function is continuous between the table points.   If that's true the functions intersect at exactly two points.  We don't really know that for sure so I'll go with:

Answer: f(x) and g(x) intersect at exactly two points.  FALSE

I may be marked wrong on this last one but I'm sticking with my answer.

Answer 2

Answer:

A and D are both true.

Step-by-step explanation:

f(x) is a quadratic. It is the graph in red. Its equation is y = (x + 3)^2

g(x) is an absolute value formula. It is the graph in blue. Its equation is y=abs(x + 3) + 1

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The last statement is correct. The two figures cross at (-1.382,2.618) and (-4.618, 2.618) so D is true. But don't stop reading. You'll learn much from this question.

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From the right intersect point to the left intersect point, the blue graph is greater than the red one. C is false. Remember the red graph is f(x)

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B is false. g(x) is a quadratic

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Unfortunately I'm getting that A is true

f(-2) = 2 and

g(-2) = 1