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New Functions from Old Functions

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Jereve Bayaborda

Philippines

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Froggy Jumps Jump into Conclusion!Online version New Functions from Old Functions by Jereve Bayaborda 1 What is the effect of a horizontal translation f(x) by +3 on the graph? a Shift right 3 units b Stretch horizontally by factor 3 c Shift left 3 units 2 If g(x)=f(x-4), how is the graph of f shifted relative to f? a Left 4 units b Up 4 units c Right 4 units 3 What is the inverse function f^{-1} supposed to do? a undo the action of f b redo the action of f c multiply outputs by -1 4 What does (f ∘ g)(x) mean in function composition? a Add the outputs of f and g b Apply f first, then g c Apply g first, then f 5 What happens to the graph of f when you replace x with -x? a Reflects across the x-axis b Reflects across the y-axis c Shifts up by 1 unit 6 How does f(x) -> a f(x) affect the graph? a Vertical shift by a units b Horizontal stretch by a c Vertical stretch by factor a 7 What is f^{-1}(x) for f(x)=x^3? a f^{-1}(x)=x^{1/3} b f^{-1}(x)=x^3 c f^{-1}(x)=3x 8 What does (f+g)(x) denote? a Difference of the functions b Sum of the functions at x c Product of the functions 9 How is vertical translation by k (upwards) expressed in f(x)? a k·f(x) b f(x)+k c f(x + k) 10 If h(x)=f(g(x)), what is true about the order of operations? a f is applied first, then g b They are multiplied c g is applied first, then f 11 This kind of transformation creates a distortion from how the original parent function looks like a rigid b non rigid c combination 12 each value of the dependent variable corresponds to exactly one value of the independent variable a surjective b well-defined c one-to-one 13 A function f has an inverse function if and only if f is one-to-one. a Always true b Sometimes true c Always false 14 If g(x) is in the domain of f, then we can calculate the value of f(g(x)). a Always true b Sometimes true c Always false 15 described by change in orientation and formation of symmetrical graphs a inverse b translation c reflection 16 make the graph narrower or shorter a compressions and shrinks b translation upwards and downwards c axes reflections 17 characterize by changes and movements a horizontal shifts b translations c vertical shifts 18 In the parent graph of the absolute value function, the reflection has no visible effect a always true b always false c sometimes true 19 To find the profit function, subtract the revenue function from the cost function. a Always true b It depends c Always false 20 Which of the following parent functions passes the horizontal line test? a Reciprocal functions b Periodic functions c Floor and ceiling functions

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Froggy Jumps

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Jump into Conclusion!Online version

by Jereve Bayaborda

What is the effect of a horizontal translation f(x) by +3 on the graph?

If g(x)=f(x-4), how is the graph of f shifted relative to f?

What is the inverse function f^{-1} supposed to do?

What does (f ∘ g)(x) mean in function composition?

What happens to the graph of f when you replace x with -x?

How does f(x) -> a f(x) affect the graph?

What is f^{-1}(x) for f(x)=x^3?

What does (f+g)(x) denote?

How is vertical translation by k (upwards) expressed in f(x)?

If h(x)=f(g(x)), what is true about the order of operations?

This kind of transformation creates a distortion from how the original parent function looks like

each value of the dependent variable corresponds to exactly one value of the independent variable

A function f has an inverse function if and only if f is one-to-one.

If g(x) is in the domain of f, then we can calculate the value of f(g(x)).

described by change in orientation and formation of symmetrical graphs

make the graph narrower or shorter

characterize by changes and movements

In the parent graph of the absolute value function, the reflection has no visible effect

To find the profit function, subtract the revenue function from the cost function.

Which of the following parent functions passes the horizontal line test?