Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match each graph with the function it represents

Answer 1

Graph Function

A f(x) = x

B f(x) = x^2

C f(x) = x^3

D f(x) = √(x - 1)

E f(x) = 1/x

To match each graph with the function it represents, we need to consider the shape of the graph and the equation of the function.

Graph A: This graph is a straight line that passes through the origin and has a slope of 1.

This indicates that the function is linear and has the following equation:

f(x) = x

Graph B: This graph is a parabola that opens upwards and has its vertex at the origin.

This indicates that the function is quadratic and has the following equation:

f(x) = x^2

Graph C: This graph is a cubic function that opens upwards and has a point of inflection at the origin.

This indicates that the function has the following equation:

f(x) = x^3

Graph D: This graph is a square root function. It has a vertical asymptote at x = 1 and a horizontal asymptote at y = 1.

This indicates that the function has the following equation:

f(x) = √(x - 1)

Graph E: This graph is a reciprocal function. It has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

This indicates that the function has the following equation:

f(x) = 1/x

Answer 2

`f(x)=√(x-1)` -----> Graph C

`f(x)=√(x)` -----> Graph A

`f(x)=√(x)-1` -----> Graph B

`f(x)=-√(x)` -----> Graph D

`f(x)=-√(x-1)` -----> Graph E

Explanation:

we have

case a)
`f(x)=√(x-1)`

Find the domain

we know that

The radicand must be greater than or equal to zero

so

`x-1\geq 0`

`x\geq 1`

The domain is the interval -----> [1,∞)

All real numbers greater than or equal to 1

The range is the interval -----> [0,∞)

All real numbers greater than or equal to 0

case b)
`f(x)=√(x)`

Find the domain

we know that

The radicand must be greater than or equal to zero

so

`x\geq 0`

The domain is the interval -----> [0,∞)

All real numbers greater than or equal to 0

The range is the interval -----> [0,∞)

All real numbers greater than or equal to 0

case c)
`f(x)=√(x)-1`

Find the domain

we know that

The radicand must be greater than or equal to zero

so

`x\geq 0`

The domain is the interval -----> [0,∞)

All real numbers greater than or equal to 0

The range is the interval -----> [-1,∞)

All real numbers greater than or equal to -1

case d)
`f(x)=-√(x)`

Find the domain

we know that

The radicand must be greater than or equal to zero

so

`x\geq 0`

The domain is the interval -----> [0,∞)

All real numbers greater than or equal to 0

The range is the interval -----> (-∞,0]

All real numbers less than or equal to 0

case e)
`f(x)=-√(x-1)`

Find the domain

we know that

The radicand must be greater than or equal to zero

so

`x-1\geq 0`

`x\geq 1`

The domain is the interval -----> [1,∞)

All real numbers greater than or equal to 1

The range is the interval -----> (-∞,0]

All real numbers less than or equal to 0