log, mn = log, m + log, n where, b > 0, b# 1, m>0, n>0 MHF4U Test 1 Date: Name: Wantat Mark: Show all steps for full marks. 1. Use the graph of function f, y = f(x) to the y = f ( x ) right, to answer the following questions. a) State the real zero(s) of the function. [1] 14 ,0 , 47 b) Is the function odd, even, or neither? Explain. [1] "" f ( - x ) = f ( x ) :it's even because it's symmetric -5 about the y-axis . c) State the total number of local maximum and/or local minimum points the graph of the function has. [1] 4 # of local max & localmin. d) State the total number of points of inflection the graph of the function has? [1] 3 e) As x - -co what does y -? [1] y- -co greater labove f) Solve f (x) > 0. [2J ( X / XER , * >OF g) Find the average rate of change of the h) Find the instantaneous rate of change of function from x = -2 to x = 5. Estimate the function at x = -3. Estimate to the to the nearest tenth of a unit. [3] nearest tenth of a unit. [3] Racist (0x = - 3) = mtangent cave (- 2, 5] = f (x2) - f( *1) = 1- 4 = w / w *2 - X1 5- (2) = -0.436. Use the equation of function f, f(x) = 2x2 + 8, to answer the following questions. a) Find the zero(s) of the function. [2] 0= 2x2+8 b) State the x-intercept(s) of the graph of the function. [1] -2.x -8 - 2 none is not real number . -+21 - 2; c) Is the function odd, even, or neither? Explain. [2] d) Find the average rate of change of the function from x = =1 to x = 2. Express as f ( x ) = 2 ( x ) 2 + 8 a non-decimal exact value in simplest form. [3] = 2 x2+8 -1=2 61)2+8 ROGve (-1, 2] = 16-4-12 = 2+8 2 -GD 3 ( - 1 ,4 ) " : f( -x ) = f ( x ) :. it's even. 2=2 ( ))+8 = 8+8 1= 16 ( 2 , 16 ) 2 (3)'+8 = 26 e) Find the instantaneous rate of change of the function at x = 3. Approximate to the nearest tenth of a unit. [3] X 6 Xotox f ( xot x ) - f ( *0 ) Roust (@ x = 3 is 12) 3.1 27.22 - 26- 12.2 3 6.01 3.01 26.1202 -26 0.01 00 12 3 0.001 3.601 25.012002-26 12.0 6,001 Page 4 of 4 MHF4U - 1 - Test - 2022202381. docx3. Use the relation {(1,5), (2,7), (4,2), (5,1). (7,7)], to answer the following questions. a) Is the relation a function? [1] yes , posses vertical line . b) State the domain of the relation. [1] (1, 2, 4, 5, 7} c) State the range of the relation. [1] ( 5 , 7, 2 , 1} 4. Evaluate each expression. [4] 2x+8 (a) As x - +00, -3x ( *+3) (x-1) - x1+2x-3/ (b) As x - 1 , a_2x41/ *(8 - 3) 3 (1+3) (1-1) (4) 60) - -0 3.9 5. Sketch the graph of y = -3 - (x - 4) + 5. [4] a= 3 med Iid h= + 4 k= 5 - 2x +4 1- 34+5 0= 5 4 = 0 2 = 1 1=2 - 4= 4 2 = - 1 - 14 = 9 3 = -4bel the key 2' Sketch the graph of the function that has the following key features and then In feamreson the ; :11, 4 maximum mint 5 at the 1an maximum Im mlnimum mint 5 at the lobal minimum [am local maximum . Int 5 \" local minimum mint 5 Amman-(S) end behaviour as .r -+ +co and behaviour as x ) an end behaviour as x ) 3' end behaviour as x -) 3' mE