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3Material AICLE 3º de ESO: Sequences (Solucionario)
• Y = x: (0,0) • Y=5x-‐7: (0,-‐7) and (7/5,0) • Y= 5: (0,5)
• Y= x2-‐4, (0,-‐4), (2,0), (-‐2,0)
• Y= 2x2+5x-‐4: (0,-‐4), (0.63,0) and (-‐2.97,0) • Y=3x2-‐x+10: (0,10)
• Y= : (0,0)
SOLUTIONS
Intersection of the graphic of a function with the Cartesian axes
1)
a) Table:
X -‐1 0 2 3 Y=x-‐3 -‐4 -‐3 -‐1 0
c) The intersection points are (0,-‐3) and (3,0)
d) Complete: the ordinate of a point on the X-‐axis is always zero. The abscissa of a point on the Y-‐axis is always zero.
2) Point of intersection (last question):
3) Text:
• The point of intersection of the graphic of a function with the X-‐axis has the form (a,0).
• May be more than one points of intersection with the X-‐axis. • To calculate this point/s you give the value zero to the first coordinate and
calculate the second one (using the algebraic expression). • The point of intersection of the graphic of a function with the Y-‐axis has the form
(b,0). • You will never find more than one point of intersection with the Y-‐axis. • To calculate this point you solve the equation y=0 (or f(x)=0 where f(x) is the
algebraic expression).
4 Material AICLE 3º de ESO: Sequences (Solucionario)
Affine functions
2)
a) Text:
• An affine function is a function that has an algebraic expression like this: y = mx+n
• The numbers of the expression are called slope (with the same meaning as in linear
functions) and ordinate at the origin (is the value of the ordinate for x=0, at the
origin).
• The relationship between slope and the increase/decrease is the same as in linear
functions.
• A linear function is an affine function whose ordinate at the origin is equal to zero.
• There can be two points of intersection with the axes, no more.
Inverse proportionality function
1)
a) The contamination level is 100. The level becomes half what is xas yesterday.
b) Y= 1200/x. The domain is every positive number, zero is not included.
c) Text:
3) The true affirmation is the third one.
A function with this algebraic expression y = a/x (a is a number different to zero) is an inverse proportionality function.
5Material AICLE 3º de ESO: Sequences (Solucionario)
4)
b) Chart:
Expressions It is function -‐-‐-‐ because…
It’s a linear function
2 because the corresponding form is y=mx
It’s an affine function
1 because the corresponding form is y=mx+n
It’s an increasing function
2 because the slope is positive
It’s an decreasing function
1 because the slope is negative
It has a symmetry axis
3 because the corresponding graphic is a hyperbola
Every number is an element of the domain of the function
1 and 2 because you can calculate the
corresponding ordinate to every value of the abscissa
It’s a function of inverse proportionality
3 because the corresponding form is y=a/x
Every number is an element of the range of the function
1 and 2 because every value of the ordinate has a
corresponding value for the abscissa
There are local or global minima or maxima
-‐
There aren’t global maximum or minima.
1,2,3, no value of the range is greater/less than the
rest
5)
a) There are not points of intersection of the graphic with the Cartesian axes.
6 Material AICLE 3º de ESO: Sequences (Solucionario)
If a=0 the function y =ax2+bx+c is not
quadratic but affine: y = bc+c
The symmetry axis of a quadratic function is parallel
to the ordinates axis (the Y-‐axis)
The two branches are symmetric
so you can draw one and copy to obtain the other.
Quadratic functions
1)
If x + m = 8, then m = 8-‐x
The product of both numbers is x ·∙ m = x(8-‐x)
y=x(8-‐x) = 8x-‐x2
The value table of the function is:
x -‐2 -‐1 0 1 2 5 8 10 100
y -‐20 -‐9 0 7 12 15 8 -‐20 -‐9200
One vertex and two branches.
3) The true affirmations are: second, fourth, fifth.
4)
a) The corrected wrong words are: quadratic, function, expression, equal, zero, sign.
b)
7Material AICLE 3º de ESO: Sequences (Solucionario)
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11Material AICLE 3º de ESO: Sequences (Solucionario)
