Section 1.2 Extra Practice
STUDENT BOOK PAGES 10–21
1. Calculate the slope of the line through each pair of
points.
a. (6, ⫺2), (3, 4)
7
4
b. a , 1b , a⫺5, b
5
6
c. (4.3, 0.7), (2, 6.1)
2. State the equation and sketch the graph of the
following lines:
a. having slope 4 and y-intercept ⫺2
b. passing through (2, 1) and (3, 6)
c. having x-intercept ⫺3 and y-intercept 7
3. Simplify the following difference quotients.
(1 ⫹ h) 2 ⫺ 1
a.
h
(9 ⫹ h) 2 ⫺ 81
b.
h
5
5
x ⫹ 2 ⫺ 2
c.
x
4. Rationalize each of the following numerators to
obtain an equivalent expression.
兹h ⫹ 49 ⫺ 7
h
兹x ⫹ 2 ⫺ 兹2
b.
x
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a.
5. Determine the slope of the tangent to each curve at
the given point.
a. y ⫽ 2x 2; (⫺2, 8)
b. y ⫽ ⫺10x ⫹ 3; (6, ⫺57)
1
1
c. y ⫽ ; a4, b
x
4
6. For the equations in question 5, use a graphing
calculator to approximate the slope.
7. Consider several different linear functions (lines of
the form y ⫽ mx ⫹ b). By finding tangent lines at a
point and using graphing technology, determine what
the slope is at every point of a linear function.
8. Determine the slope of the tangent to each curve at
the point which is given below.
a. y ⫽ 兹x ⫹ 4 at (5, 3)
b. y ⫽ 兹x ⫺ 1 at (26, 5)
c. y ⫽ 兹2x ⫺ 3 at (2, 1)
9. Determine the slope of the tangent to each curve at
the point which is given below.
3
a. y ⫽ ; x ⫽ ⫺4
x
5
b. y ⫽
;x⫽1
2⫹x
10
c. y ⫽ ⫺
; x ⫽ ⫺5
10 ⫹ x
10. Determine the slope of the tangent to each curve at
the point whose x-value is given.
a. f (x) ⫽ x 2 ⫺ 4x; x ⫽ 1
20
1
b. f (x) ⫽
;x⫽
x
2
c. f (x) ⫽ 2x 2; x ⫽ ⫺1
d. f (x) ⫽ 兹x ⫺ 11; x ⫽ 15
11. Show that, at the point of intersection of the cubic
functions f (x) ⫽ x 3 and g (x) ⫽ 14 ⫺ x 3, the slopes
of the tangents to each function are negatives of
each other.
Section 1.2 Extra Practice
325