Worksheet: Intercepts and Symmetry of Graphs of Functions

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In this worksheet, we will practice interpreting the intercepts of a graph and determining the symmetry of functions.

Q1:

In the graph below, find the axis of symmetry.

  • AThe 𝑦-axis
  • BThe origin
  • CThe 𝑥-axis

Q2:

In the graph below, find the axis of symmetry.

  • Athe 𝑥-axis
  • Bthe 𝑦-axis
  • Cthe origin

Q3:

In the graph below, find the axis of symmetry.

  • AThe 𝑥-axis
  • BThe origin
  • CThe 𝑦-axis

Q4:

Given that 𝑓(𝑥)=−9𝑥𝑥<0,9𝑥𝑥>0.ifif About which point is the function symmetric?

  • A ( 9 , − 9 )
  • B ( 0 , 9 )
  • C ( 0 , 0 )
  • D ( − 9 , 0 )

Q5:

Find the point of symmetry of the function 𝑓(𝑥)=1𝑥−2−1.

  • A ( − 1 , − 2 )
  • B ( 2 , − 1 )
  • C ( − 2 , − 1 )
  • D ( − 1 , 2 )

Q6:

If the function 𝑓(𝑥)=1𝑥, determine the point of symmetry of the function 𝑓(𝑥−7).

  • A ( − 7 , 0 )
  • B ( 0 , 7 )
  • C ( 7 , 0 )
  • D ( 0 , − 7 )

Q7:

What are the 𝑥-intercepts of the function represented by the given graph?

  • A ( − 1 , 0 ) and (0,2)
  • B ( − 1 , 0 ) and (2,0)
  • C ( 0 , − 1 ) and (0,2)
  • D − 1 , 1 2 and 2,12
  • E ( 0 , − 1 ) and (2,0)

Q8:

In the graph shown, find the axis of symmetry.

  • A 𝑥 = 1
  • B 𝑥 = − 4
  • C 𝑥 = − 3
  • D 𝑥 = 3
  • E 𝑥 = 5

Q9:

What are the 𝑥-intercepts of the function represented by the given graph?

  • A ( − 1 , 3 ) and (3,3)
  • B ( − 1 , 0 ) and (3,0)
  • C ( 0 , − 1 ) and (0,3)
  • D ( 0 , − 1 ) and (3,0)
  • E ( − 1 , 0 ) and (0,3)

Q10:

In the graph shown, find the axis of symmetry.

  • A 𝑥 = 2
  • B 𝑥 = − 2
  • C 𝑥 = 1
  • D 𝑥 = − 1
  • E 𝑥 = 5

Q11:

Determine the intercepts of the function represented by the given graph.

  • A 𝑥 -intercept: (0,2), 𝑦-intercept: (0,3)
  • B 𝑥 -intercept: (0,3), 𝑦-intercept: (2,0)
  • C 𝑥 -intercept: (2,0), 𝑦-intercept: (3,0)
  • D 𝑥 -intercept: (0,2), 𝑦-intercept: (3,0)
  • E 𝑥 -intercept: (2,0), 𝑦-intercept: (0,3)

Q12:

What is the 𝑦-intercept of the function represented by the given graph?

  • A ( 0 , 2 )
  • B ( 2 , 0 )
  • C ( − 1 , 0 )
  • D ( − 2 , 0 )
  • E ( 0 , − 2 )

Q13:

What is the 𝑦-intercept of the function represented by the given graph?

  • A ( − 1 0 , − 2 )
  • B ( 0 , − 2 )
  • C ( − 2 , 0 )
  • D ( − 1 0 , 0 )
  • E ( 0 , − 1 0 )

Q14:

Find the horizontal intercepts of the function 𝑓(𝑥)=2|𝑥+2|−10.

  • A 𝑥 = 3 , − 7
  • B 𝑥 = − 3 , 7
  • C 𝑥 = 5 , − 5
  • DNo horizontal intercepts

Q15:

The diagram shows the graph of 𝑦=𝑓(𝑥). What is the solution set of the equation 𝑓(𝑥)=0?

  • A ∅
  • B { 1 }
  • C { 4 }
  • D { − 1 }
  • E { − 3 , 1 }

Q16:

A function 𝑡(𝑥) has 𝑥-intercepts at −4 and 9. Where are the intercepts of 𝑡(𝑥−5)?

  • Aat −9 and 4
  • Bat 1 and 14
  • Cat 20 and −45
  • Dat −4 and 9

Q17:

The diagram shows the graph of 𝑦=𝑓(𝑥). What is the solution set of the equation 𝑓(𝑥)=0?

  • A { 2 , − 2 }
  • B { 2 }
  • C { 4 }
  • D { 4 , − 4 }
  • E ∅

Q18:

At which values of 𝑥 does the graph of the equation 𝑦=𝑥(𝑥−10) cross the 𝑥-axis?

  • A √ 1 0 and −√10
  • B0 and −√10
  • C0 and √10
  • D0 and −10
  • E0 and 10

Q19:

At which values of 𝑥 does the graph of the equation 𝑦=(𝑥+2)(𝑥−6) cross the 𝑥-axis?

  • A4 and 12
  • B4 and −12
  • C − 4 and −12
  • D2 and −6
  • E − 2 and 6

Q20:

Factor the equation 𝑦=𝑥−9.

  • A 𝑦 = ( 𝑥 − 3 ) ( 𝑥 − 3 )
  • B 𝑦 = ( 𝑥 + 9 ) ( 𝑥 − 9 )
  • C 𝑦 = ( 𝑥 + 4 . 5 ) ( 𝑥 − 4 . 5 )
  • D 𝑦 = ( 𝑥 + 3 ) ( 𝑥 − 3 )
  • E 𝑦 = ( 𝑥 − 4 . 5 ) ( 𝑥 − 4 . 5 )

At which values of 𝑥 does the graph of 𝑦=𝑥−9 cross the 𝑥-axis?

  • A4.5
  • B3 and −3
  • C4.5 and −4.5
  • D3
  • E9 and −9

Q21:

At which values of 𝑥 does the graph of the equation 𝑦=(3𝑥−2)(𝑥+1) cross the 𝑥-axis?

  • A − 2 and 1
  • B − 2 3 and 1
  • C 2 3 and −1
  • D2 and −1
  • E 3 2 and −1

Q22:

Factor fully the equation 𝑦=5𝑥−45.

  • A 5 ( 𝑥 + 3 ) ( 𝑥 − 3 )
  • B ( 𝑥 + 3 ) ( 𝑥 − 3 )
  • C ( 𝑥 + 1 ) ( 𝑥 − 9 )
  • D 5 ( 𝑥 + 1 ) ( 𝑥 − 9 )
  • E ( 𝑥 + 5 ) ( 𝑥 − 9 )

At which values of 𝑥 does the graph of 𝑦=5𝑥−45 cross the 𝑥-axis?

  • A5 and −9
  • B9 and −5
  • C9 and −1
  • D1 and −9
  • E3 and −3

Q23:

At which values of 𝑥 does the graph of the equation 𝑦=−(𝑥−3)(𝑥+8) cross the 𝑥-axis?

  • A − 3 and 8
  • B − 3 and −8
  • C − 5 and 24
  • D3 and −8
  • E5 and −24

Q24:

At which values of 𝑥 does the graph of the equation 𝑦=5(𝑥−1)(𝑥+7) cross the 𝑥-axis?

  • A5 and −7
  • B − 1 and 7
  • C − 7 and 6
  • D7 and −6
  • E1 and −7

Q25:

At which values of 𝑥 does the graph of 𝑦=4𝑥−20 cross the 𝑥-axis?

  • A2.5 and −2.5
  • B √ 5 and −√5
  • C5 and −5
  • D4 and −4
  • E − 2 0

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