Free Printable Chapter 1 TEST

1.

Write the equation of the line (in point-slope form) that has function values $f\left(4\right)=-8\ and\ f\left(-2\right)=4$

a)

$y-4=-2\left(x+2\right)$

b)

$y-4=-\frac{1}{2}\left(x+2\right)$

c)

$y+2=-2\left(x-4\right)$

d)

$y+2=-\frac{1}{2}\left(x-4\right)$

2.

Write the equation of the line parallel to the graph of 2y - 6 = 0 and passing through (4, -1).

a)

x = 4

b)

x = -1

c)

y = -1

d)

y = 4

3.

Find the x and y intercepts of: $y-6=x^2-5x$

a)

x-int: (-1, 0), (6, 0); y-int: (0, 6)

b)

x-int: (6, 0), (11, 0); y-int: (0, -6)

c)

x-int: (2, 0), (3, 0); y-int: (0, 6)

d)

x-int: (0, 0), (5, 0); y-int: (0, -6)

4.

Find the standard form equation of the circle whose endpoints of a diameter are at (4, 3) and (0, 1).

a)

$\left(x-2\right)^2+\left(y-1\right)^2=5$

b)

$\left(x-2\right)^2+\left(y-2\right)^2=5$

c)

$x^2+\left(y-1\right)^2=\sqrt{5}$

d)

$\left(x-4\right)^2+\left(y-3\right)^2=\sqrt{5}$

5.

What is the radius of the given circle: $x^2+y^2-10x+8y-23=0$ ?

a)

2

b)

4

c)

8

d)

$\frac{23}{2}$

6.

Is the relation a function? Why/Why Not?

a)

Yes, because the x-value 11 has two y-values.

b)

Yes, because each x-value has only one y-value.

c)

No, because the x-value 11 has two y-values.

d)

No, because each x-value has only one y-value.

7.

Find the domain of: $g\left(x\right)=\sqrt{5-3x}$

a)

$\left(-\infty,\ 0\right)\left(0,\ \infty\right)$

b)

$\left[\frac{5}{3},\ \infty\right)$

c)

$\left(-\infty,\ 0\right]$

d)

$\left(-\infty,\ \frac{5}{3}\right]$

8.

Find the domain of: $f\left(x\right)=\frac{2x}{3x^2-16x+21}$

a)

$\left(-\infty,\ \frac{7}{3}\right)\left(\frac{7}{3},\ 3\right)\left(3,\ \infty\right)$

b)

$\left(-\infty,\ 1\right)\left(1,\ 7\right)\left(7,\ \infty\right)$

c)

$\left(-\infty,\ 0\right)\left(0,\ \infty\right)$

d)

$\left(-\infty,\ 3\right)\left(3,\ \infty\right)$

9.

Find the domain of: $h\left(x\right)=\frac{x}{9}$

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,\ 0\right)\left(0,\ \infty\right)$

c)

$\left(-\infty,\ 9\right)\left(9,\ \infty\right)$

d)

$\left[0,\ \infty\right)$

10.

If $f\left(x\right)=3x-1$ and $g\left(x\right)=x^2+2$
what is $\left(g\ \circ\ f\right)\left(x\right)$ ?

a)

3x² + 5

b)

9x² - 6x + 3

c)

3x² - 6x + 1

d)

3x² + 3

11.

Given $f\left(x\right)=1+x-2x^2$ , find $\frac{f\left(x+h\right)-f\left(x\right)}{h},\ h\ne0$

a)

$1-4x-2h,\ h\ne0$

b)

$1,\ h\ne0$

c)

$\frac{2x+h-4x^2-4xh-2h^2}{h},\ h\ne0$

d)

$1+2x+h,\ h\ne0$

12.

$f\left(x\right)=2x^2-x\ and\ g\left(x\right)=3x-5$ find $3\left(f+g\right)\left(x\right)-2g\left(x\right)$

a)

$2x^2-4x+5$

b)

$2x^2+3x-10$

c)

$6x^2-5$

d)

$6x^2-25$

13.

Find the average rate of change of the function $f\left(x\right)=6-\sqrt{1-x}$ from $x_1=-3\ to\ x_2=0$

a)

$-3$

b)

$3$

c)

$-\frac{1}{3}$

d)

$\frac{1}{3}$

14.

Find the zero(s) of:
$h\left(x\right)=\frac{2x+1}{15-x}$

a)

$x=-\frac{1}{2};\ x=15$

b)

$x=-\frac{1}{2}$

c)

$x=\frac{1}{2};\ x=-15$

d)

$x=15$

15.

Write the area of a circle as a function of its diameter.
$\left(A=\pi r^2\right)$

a)

$A\left(d\right)=4\pi d^2$

b)

$d=\frac{1}{2}\sqrt{\frac{A}{\pi}}$

c)

$A\left(d\right)=\frac{\pi d^2}{4}$

d)

$A\left(d\right)=\pi d^2$

16.

Write the height of the rectangle as a function of x.

a)

$x^2+\frac{1}{2}x-2$

b)

$-2+\frac{1}{2}x-x^2$

c)

$2-\frac{1}{2}x-x^2$

d)

$\frac{3}{2}x-x^2$

17.

Which piecewise function matches the graph shown?

a)

b)

c)

d)

18.

A piecewise function, f(x), is shown in the graph. What is the value of $f\left(-4\right)$ ?

a)

-4

b)

-2

c)

0

d)

Does not exist

19.

Graph:

$f\left(x\right)=-\left[\left[\frac{1}{2}x\right]\right]$

a)

b)

c)

d)

20.

Determine the intervals over which the function is increasing, decreasing, or constant.

a)

Decreasing: $\left(-\infty,\ -4\right]\left[0,1\right]\left[5,8\right]$ Constant: $\left[-3,\ 0\right]$ Increasing: $\left[-4,\ -3\right]\left[1,\ 5\right]\left[8,\ \infty\right)$

b)

Decreasing: $\left(-\infty,\ -3\right)\left(0,\ -1\right)\left(7,\ -2\right)$ Constant: $\left(0,\ 0\right)$ Increasing: $\left(-3,\ 0\right)\left(-1,\ 7\right)\left(-2,\ \infty\right)$

c)

Decreasing: $\left(\infty,\ -4\right)\left(5,\ 8\right)$ Constant: $\left(-3,\ 0\right)$ Increasing: $\left(-4,\ -3\right)\left(1,\ 5\right)\left(8,\ \infty\right)$

d)

Decreasing: $\left(-\infty,\ -4\right)\left(0,\ 1\right)\left(5,\ 8\right)$ Constant: $\left(-3,\ 0\right)$ Increasing: $\left(-4,\ -3\right)\left(1,\ 5\right)\left(8,\ \infty\right)$

21.

Given $f\left(x\right)=2\left[\left[x\right]\right]-7$ find $f\left(-\frac{5}{2}\right)$

a)

-13

b)

-11

c)

-3

d)

-1

22.

Let g be a vertical stretch by a factor of 2 followed by a translation 6 units left of the graph given by f(x). Write a rule for g.
$f\left(x\right)=\left|x\right|-3$

a)

$g\left(x\right)=2\left|x+6\right|-6$

b)

$f\left(x\right)=2\left|x\right|-9$

c)

$f\left(x\right)=2\left|x+6\right|-3$

d)

$f\left(x\right)=2\left|x-6\right|-3$

23.

Let $f\left(x\right)=x^2-1$ . Given $g\left(x\right)=-\frac{1}{2}f\left(x+6\right)$ . Write a rule for g.

a)

$g\left(x\right)=-\frac{1}{2}x^2+5$

b)

$g\left(x\right)=-\frac{1}{2}\left(x+6\right)^2-1$

c)

$g\left(x\right)=-\frac{1}{2}\left(x+6\right)^2+\frac{1}{2}$

d)

$g\left(x\right)=-\frac{1}{2}x^2+\frac{13}{2}$

24.

Find a mathematical model to represent the statement: v varies directly as the square root of s (v = 24; s = 16).

a)

$v=kx^2$

b)

$v=6\sqrt{x}$

c)

$v=k\sqrt{x}$

d)

$v=\frac{3}{128}x^2$

25.

A company has found that the daily demand x for its boxes of chocolates is inversely proportional to the price p. When the price is $5, the demand is 800 boxes. Approximate (to the nearest whole value) the demand when the price is increased to $6.

a)

667 boxes of chocolates

b)

960 boxes of chocolates

c)

4000 boxes of chocolates

d)

27 boxes of chocolates

26.

The number of kilograms of water in a person’s body varies directly as the person’s mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a person whose mass is 75 kg?

a)

50 kg water

b)

72 kg water

c)

94 kg water

d)

150 kg water

27.

A passenger stranded on a lifeboat shoots a distress flare into the air. The height (in feet) of the flare above the water is given by $f\left(x\right)=-16x^2+128x$ , where x is the time (in seconds) since the flare was shot. What is the maximum height of the flare?

a)

4 ft.

b)

128 ft.

c)

144 ft.

d)

256 ft.

Chapter 1 TEST

Total questions: 27

Worksheet time: 3hrs 40mins

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