Domain and range

Sketch a graph to help figure it out Domain: The domain is the set of all possible x-values which will make the function "work", and will output real y-values. Range: The range is the resulting y-values we get after substituting all the possible x-values Sketch a graph to help figure it out Range Domain

Domain and range co-joined functions Ten questions Domain and range co-joined functions

State the range of this function 𝑓 𝑥 = 2𝑥−4 14−𝑥 2≤𝑥<6 6≤𝑥≤14 The function is the line between 2 and 6 and the 2nd straight line between 6 and 14 Range 0≤𝑦≤8 Domain 2≤𝑥≤14

State the range of this function The function is the line between 0 and 2 and the 2nd straight line between 2 and 8 𝑓 𝑥 = 𝑥+4 4−𝑥 0≤𝑥<2 2≤𝑥≤8 Range 𝟎≤𝑦≤6 Domain 0≤𝑥≤8

State the range of this function The function is the curve between -1 and 4 𝑓 𝑥 = 𝑥 2 −4𝑥+3 −1<𝑥≤4 Range −1<𝑦≤8 Domain −1<𝑥≤4

State the range of this function The function is the curved graph between 0 and 3 and the straight line between 3 and 8 𝑓 𝑥 = 𝑥−1 2 +2 6 0≤𝑥<3 3≤𝑥≤8 Range 2≤𝑦≤6 Domain 0≤𝑥≤8

Solve f(x) = 3 using a graph 5 of 10 Solve f(x) = 3 using a graph 𝑓 𝑥 = 𝑥 2 −2𝑥 8 −2≤𝑥<4 4≤ 𝑥≤8 The function is the curve between -2 and 4 and the straight line between 4 and 8 𝑓 𝑥 =3 at two points on the graph When 𝑥=−1 And 𝑥= 3 −1, 3 3, 3

6 of 10 Define this function given by this graph The function is the straight line between 0 and 3 and the curved graph between 3 and 7 𝑦=−𝑥 2 +8𝑥−11 Range −4≤𝑦≤5 Domain 0≤𝑥≤7 𝑓 𝑥 = 4 −𝑥 2 +8𝑥−11 0≤𝑥<3 3≤𝑥≤7

State the range of this function The function is the curve between 2 and 7 and the 2nd curve between 7 and 11 𝑓 𝑥 = 6− (𝑥−5) 2 𝑥 2 −18𝑥+79 2≤𝑥<7 7≤𝑥≤11 Range −3≤𝑦≤6 Domain 2≤𝑥≤11

𝑓 𝑥 = (𝑥+2) 2 +1 5− 1 2 𝑥 −1≤𝑥<3 3≤𝑥≤5 8 of 10 Define this function given by this graph The function is the straight line between -1 and 3 and the curved graph between 3 and 5 (𝑥+2) 2 +1 5 − 1 2 𝑥 Range 0≤𝑦≤5 Domain −4≤𝑥≤10 𝑓 𝑥 = (𝑥+2) 2 +1 5− 1 2 𝑥 −1≤𝑥<3 3≤𝑥≤5

State the range of this function The function is the straight line between 0 and 3 and the curved graph between 3 and 7 𝑓 𝑥 = 4 −𝑥 2 +8𝑥−11 0≤𝑥<3 3≤𝑥≤7 Range 0≤𝑦≤6 Domain −4≤𝑥≤5

10 of 10 Define this function given by this graph The function is the straight line between -1 and 3 and the curved graph between 3 and 5 −𝑥 2 +6𝑥−3 Range −2≤𝑦≤6 Domain −1≤𝑥≤5 𝑓 𝑥 = 2𝑥 −𝑥 2 +6𝑥−3 −1≤𝑥<3 3≤𝑥≤5

One thing to improve is – KUS objectives BAT understand domain and range of functions BAT define functions from graphs self-assess One thing learned is – One thing to improve is –

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