Combination of Graphs (Junior Cert Mathematics): Quizzes

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Combination of Graphs
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What does it mean graphically when two functions are equal?

Their graphs cross each other

At what points do f(x)=x22xf(x) = x^2 - 2x and g(x)=x2g(x) = x - 2 intersect?

x=1x = 1 and x=2x = 2

What shape is a parabola?

U-shaped curve

At intersection points, what is true about the two functions?

Same output for same input

What does f(x)<g(x)f(x) < g(x) mean graphically?

Graph of f(x)f(x) is below g(x)g(x)

For what xx-values is f(x)=x26x+5f(x) = x^2 - 6x + 5 less than g(x)=x1g(x) = x - 1?

1<x<61 < x < 6

Why does a graph below another mean its function is less?

Lower graph has smaller outputs

At what points do f(x)=x26x+5f(x) = x^2 - 6x + 5 and g(x)=x1g(x) = x - 1 intersect?

x=1x = 1 and x=6x = 6

What is a key benefit of using graphs to solve function problems?

Visual representation of relationships

How do graphs help compare functions?

Quickly spot intersections & overlaps

What should be clearly labeled on function graphs?

xx-axis, yy-axis & important points

What tool helps ensure graphs are drawn accurately?

Graph paper

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