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SAT Math : Algebra

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Example Questions

Example Question #46 : Algebraic Functions

A jet goes from City 1 to City 2 at an average speed of 600 miles per hour, and returns along the same path at an average speed if 300 miles per hour. What is the average speed, in miles per hour, for the trip?

Possible Answers:

450miles/hour

400miles/hour

350miles/hour

300miles/hour

500miles/hour

Correct answer:

400miles/hour

Explanation:

Chose a number for the distance between City 1 and 2; 1800 works well, as it is a multiple of 600 and 300.

Now, find the time for each trip, the total distance, and the total time.

$t_1=\frac{d_1}{v_1}=\frac{1800}{600}=3$

$t_2=\frac{d_2}{v_2}=\frac{1800}{300}=6$

$total\ t=t_1+t_2=3+6=9$

$total\ d=d_1+d_2=1800+1800=3600$

Now we can find the average speed by dividing the total distance by the total time.

$average speed = \frac{total distance}{total time} = \frac{3600 miles}{9 hours} = 400 miles/hour$

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Example Question #47 : Algebraic Functions

$f(x)=3x^{2}-5$

g(x)=9-2x

Find f(g(5)) .

Possible Answers:

131

Correct answer:

Explanation:

Plug 5 into g(x) first:

g(5)=9-2(5)

=-1

Now, plug this answer into f(x) :

$f(-1)=3(-1)^{2}-5$

=3-5

=-2

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Example Question #48 : Algebraic Functions

If f(x) = 3x + 7 and g(x) = x^2 - 12 , what is f(g(x)) ?

Possible Answers:

3x^2 + 29

3x^3 - 29

3x^2 - 29

9x^2 - 29

9x^3 + 29

Correct answer:

3x^2 - 29

Explanation:

Plug g(x) into f(x) as if it is just a variable. This gives f(g(x)) = 3(x²– 12) + 7.

Distribute the 3: 3x²– 36 + 7 = 3x²– 29

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Example Question #1054 : Algebra

Some values of the function are given in the table above.

For which of the following values of does g(b) equal $\left|\frac{1}{2}b\right| + 3$ ?

Possible Answers:

Correct answer:

Explanation:

If $\left|\frac{1}{2}b\right| + 3$ , then

$\left| \frac{1}{2}(-2)\right| + 3 = 4$ ,

so must be the correct choice.

When we try the other values for b, our g(b) does not match.

We can verify by trying the other possible answer choices as follows.

$\left| \frac{1}{2}(0)\right| + 3 =3 \ne-1$

$\left| \frac{1}{2}(1)\right| + 3 =4 \ne5$

$\left| \frac{1}{2}(-1)\right| + 3 =3.5 \ne 0$

And b=2 is not a value on the table provided thus it is not a correct answer.

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Example Question #81 : How To Find F(X)

f(x) = 4x + 17

Solve f(x) for the equation above for x = 3.

Possible Answers:

Correct answer:

Explanation:

The correct answer is 29. We plug in 3 into the equation above and solve for x. So we find that f(x) = 4(3) + 17. 12 + 17 = 29

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Example Question #86 : How To Find F(X)

Define a function as follows:

f(x) = |2x - 7| + 19 .

If f(c)= f(3) and $c \ne 3$ , evaluate .

Possible Answers:

c= 16

c= 23

c= -3

c= 4

c= -4

Correct answer:

c= 4

Explanation:

f(x) = |2x - 7| + 19 , so

$f(3) = |2 \cdot 3 - 7| + 19 = |6-7 | + 19 = |-1| + 19 = 1 + 19 = 20$

Therefore, solve the equation

f(c)=20 for :

|2c - 7| + 19 = 20

|2c - 7| + 19- 19 = 20 - 19

|2c - 7| =1

Either 2c-7 = -1 or 2c-7 = 1 ; solve each.

2c-7 = -1

2c-7 + 7 = -1+ 7

2c = 6

c= 3 , which we toss out:

2c-7 = 1

2c-7 +7= 1+7

2c = 8

c = 4 , which we accept.

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Example Question #1056 : Algebra

Function 4

Define to be the function graphed above.

Give the -intercept of the graph of the function , which is defined as

g(x) = 5 - f(x) .

Possible Answers:

(0, -1)

(0, -9)

(0,1)

(0,9)

$\left ( 0, -\frac{1}{2} \right )$

Correct answer:

(0,9)

Explanation:

The -intercept of a function is the point at which x = 0 , so we can find this by evaluating g(0) .

g(x) = 5 - f(x)

g(0) = 5 - f(0)

From the diagram, it can be seen that f(0) = -4 , so

g(0) = 5 - (-4) = 9

The -intercept of the graph of is (0,9) .

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Example Question #1056 : Algebra

Function 4

Define to be the function graphed above.

Give the -intercept of the graph of the function , which is defined as

g(x) = f(4x) .

Possible Answers:

(0, 1)

(0, 8)

The correct answer is not given among the other four responses.

(0,0)

(0, 16)

Correct answer:

The correct answer is not given among the other four responses.

Explanation:

The -intercept of a function is the point at which x = 0 , so we can find this by evaluating g(0) .

g(x) = f(4x)

$g(0) = f(4 \cdot 0) = f (0)$

From the diagram, it can be seen that f(0) = -4 , so g(0) = -4 , and the -intercept of the graph of the function is the point (0, -4) . This is not among the given responses.

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Example Question #87 : How To Find F(X)

Function 4

Define to be the function graphed above.

Which of the following is an -intercept of the graph of the function , if is defined as

g(x)= f(x)+3 ?

Possible Answers:

$\left ( 2 \frac{1}{2}, 0\right )$

The graph of has no -intercept.

(-1,0)

$\left ( -6 \frac{1}{2}, 0\right )$

$\left ( - \frac{1}{2}, 0\right )$

Correct answer:

$\left ( - \frac{1}{2}, 0\right )$

Explanation:

An -intercept of the graph of has as its -coordinate a value such that

g(x) = 0 ,

or, equivalently,

f(x)+3 = 0

f(x) = -3

From the diagram below, it can be seen that if f(x) = -3 , then $x =-\frac{1}{2}$ or x = 2 .

Function 4a

Therefore, the graph of has two -intercepts, $\left ( - \frac{1}{2}, 0\right )$ and (2, 0) .

The correct choice is therefore $\left ( - \frac{1}{2}, 0\right )$ .

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Example Question #86 : How To Find F(X)

Function 4

Define to be the function graphed above.

Give the -intercept of the graph of the function , which is defined as

g(x) = f(x+ 3)

Possible Answers:

(0, -2)

$\left ( 0, -2 \frac{1}{2}\right )$

The graph of has no -intercept.

(0, -6)

(0,2)

Correct answer:

$\left ( 0, -2 \frac{1}{2}\right )$

Explanation:

The -intercept of a function is the point at which x = 0 , so we can find this by evaluating g(0) .

g(x) = f(x+ 3)

g(0) = f(0+ 3) = f(3)

As can be seen in the diagram below, $f(3) = -2\frac{1}{2}$ .

Function 4a

The -intercept is $\left ( 0, -2 \frac{1}{2}\right )$ .

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SAT Math : Algebra

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #46 : Algebraic Functions

Example Question #47 : Algebraic Functions

Example Question #48 : Algebraic Functions

Example Question #1054 : Algebra

Example Question #81 : How To Find F(X)

Example Question #86 : How To Find F(X)

Example Question #1056 : Algebra

Example Question #1056 : Algebra

Example Question #87 : How To Find F(X)

Example Question #86 : How To Find F(X)

All SAT Math Resources

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